OPINION
PER CURIAM.
The False Claims Act (FCA) creates a civil cause of action against “any person who ... knowingly presents, or causes to be presented, a false or fraudulent claim for payment” to the United States Government. 31 U.S.C. § 3729(a). Claims for fraudulent Medicare billing were brought against Community Health Systems, Inc. (CHS), and in 2014, CHS, the Government, and seven “relators”—that is, private persons who bring civil actions for violations of the FCA—reached a settlement agreement. This agreement concluded years of [411]*411investigation and litigation, during which time the relators performed thousands of hours of work at the Government’s behest. CHS agreed to pay the Government and relators $88 million dollars in exchange for dismissing their claims.
This appeal centers on whether CHS failed to preserve its right to challenge the entitlement of the seven relators to attorneys’ fees. The district court adopted rela-tors’ interpretation of the settlement agreement, concluding that it unambiguously restricted CHS’s challenges to 31 U.S.C. § 3730(d), and thus limited CHS’s objections to the reasonableness of—rather than entitlement to—appellees’ attorneys’ fees. CHS appealed this decision, raising various principles of contract interpretation. Because the settlement agreement is ambiguous, we reverse the district court’s order and remand for further proceedings in the district court.
I.
Causes of action authorized by the FCA under 31 U.S.C. § 3729 have the goal of punishing and preventing fraudulent claims for payment from the U.S. Government. See United States v. Bornstein, 423 U.S. 303, 309 n.5, 96 S.Ct. 523, 46 L.Ed.2d 514 (1976). The statutory scheme includes a qui tam provision, under which a private person—a “relator”—may bring a civil action “in the name of the Government.” 31 U.S.C. § 3730(b)(1). After a relator files a sealed complaint, the Government may “proceed with the action, in which case the action shall be conducted by the Government,” or “notify the court that it declines to take over the action, in which case the person bringing the action shall have the right to conduct the action.” Id. § 3730(b)(4).
The qui tam provision is essential to achieving the FCA’s purpose “[bjecause the scope of fraud against the government is much broader than the government’s ability to detect it.” United States v. Health Possibilities, P.S.C., 207 F.3d 335, 340 (6th Cir. 2000). The FCA thus “provides private actors with a variety of incentives to bring qui tam actions, and significant influence over the ensuing development of qui tam suits—including ‘the right to conduct the action’ when the government decides not to intervene.” Id. The FCA also recognizes that relators will not come forward (risking, in many cases, their livelihoods), and private attorneys will not undertake the extensive work and expense necessary to represent relators, if they are not fairly compensated for doing so. The Act therefore provides that even if the Government takes over the action, the relator is entitled to a share of “the proceeds of the action or settlement of the claim” and his or her attorney is entitled to “reasonable attorneys’ fees and costs.” 31 U.S.C. § 3730(d)(1).
This FCA case involves seven different qui tam complaints, all of which alleged that CHS defrauded the Government by admitting Medicare patients for medically-unnecessary emergency room visits. The first four complaints were filed under seal between 2009 and 2011 in Illinois, Indiana, and Texas. In early 2011, the Government first told the relators in these four cases of the similarities among their qui tam suits, which had “triggered a nationwide investigation on the part of the U.S.” The Government encouraged these relators “to work together on the cases and share any proceeds that might result.” At the Government’s request, these relators then reached a sharing agreement in April 2011.
Appellees are three relators who were not involved in the original four cases. Appellees met with officials from the U.S. Department of Justice in Washington, D.C., U.S. Attorney’s Office for the East-[412]*412era District of Pennsylvania, and U.S. Attorney’s Office for the Middle District of Tennessee between February 2011 and April 2011. They disclosed the results of their investigation, begun in October 2010, which included “an original, robust statistical analysis of CHS admission practices” and an “extensive factual investigation.” Their statistical analysis covered 74 different hospitals. To develop the facts of CHS's alleged fraud, they “contacted approximately 100 current and former doctors and nurses at approximately 20 CHS facilities in nine states.”
In May 2011, these three relators (hereinafter Tennessee Relators) filed suit under seal in the Middle District of Tennessee. The Government then partially unsealed the four other qui tam complaints to the Tennessee Relators for their review and requested that they “actively participate in its investigation, which was led by the U.S. Attorney’s Office in Nashville, on an on-going basis.” Counsel for relators thereafter engaged in a “collaborative effort” involving “bimonthly calls with the Government.” “The Government lawyers mapped out the investigation and assigned work to all rela-tors’ counsel in an organized manner,” with “the majority of the assignments [being] made without regard to the individual complaint.” At the Government’s request, from 2011 to 2014 the Tennessee Relators’ counsel organized and analyzed thousands of documents produced by CHS, drafted letters and memoranda related to these documents, created lists of witnesses, drafted outlines for questioning witnesses, and conducted extensive legal and factual research. All told, they calculated their work on the case at nearly 7,000 billable hours.
Three years later, in the spring of 2014, the Government informed relators of a “handshake” deal with CHS. Because CHS required that, as part of settlement, all of the qui tam complaints—now seven in total—be dismissed with prejudice, the Government urged the Tennessee Relators to join the original relators’ sharing agreement. After private mediation in early May 2014, relators in all seven cases reached a sharing agreement.
The Government intervened in each of the relators’ actions on July 24, 2014. The Government filed a notice of settlement on August 4, 2014, and the district court unsealed the case. The settlement agreement provided that the Government and the seven relators would dismiss their claims upon payment by CHS of $88 million. As provided in § 3730(d), the Government awarded 19 percent of the total recovery to the relators, or about $16.4 million. See 31 U.S. § 3730(d) (“If the Government proceeds with an action brought by a person under subsection (b), such person shall ... receive at least 16 percent but not more than 26 percent of the proceeds of the action or settlement of the claim.... ”). This sum was split among all the individual relators in the various cases according to the sharing agreement that relators had reached before the settlement was finalized. The Tennessee Relators collectively received a 14 percent share, or about $2.3 million.
Pursuant to the settlement agreement, the district court dismissed the claims in October 2014, but retained jurisdiction to decide “statutory attorneys’ fees and costs pursuant to 31 U.S.C. § 3730(d).” Between October 2014 and January 2016, three district courts in Texas and Indiana transferred their cases to the Middle District of Tennessee for resolution of fee disputes. In February 2016, the court consolidated the fee disputes in the four cases before it. The court subsequently ordered the parties to brief “whether all or some of the relators are precluded from recovery of [413]*413attorneys’ fees and costs by the first-to-ffle rule provided in 31 U.S.C. § 3730(b)(5) and/or by the public disclosure bar.”
CHS argued that Term 8 of the agreement preserved its right to make first-to-ffle and public-disclosure challenges. The relevant sentence in Term 8 reads as follows: “All Parties agree that nothing in this Paragraph or this Agreement shall be construed in any way to release, waive or otherwise affect the ability of CHS to challenge or object to Relators’ claims for attorneys’ fees, expenses, and costs pursuant to 31 U.S.C. § 3730(d).” Tennessee Rela-tors argued that the phrase “pursuant to 31 U.S.C. § 3730(d)” limited the scope of CHS’s objections to those listed in that provision. Because first-to-file and public-disclosure challenges are located in § 3730(b)(5) and § 3730(e)(4) respectively, not § 3730(d), Tennessee Relators reasoned that CHS failed to preserve those challenges with the relevant language in Term 8.
After briefing and oral argument, the district court adopted relators’ interpretation of the agreement. It observed that the Government’s reservation of FCA challenges in Term 7 included specific statutory references:
Defendants could easily have specified that they intended to raise a challenge to Plaintiffs’ entitlement to fees under the first-to-file or public disclosure provisions, or, at a minimum, simply cited Section 3730(b)(5) and (e)(4), much like the Government reserved specific statutory rights and negotiated a carve-out for those provisions.
“Given the stakes,” the court reasoned, “it is difficult to believe that failure to mention the FCA’s first-to-file provision .,. anywhere in the 16-page Settlement Agreement was unintentional.” Indeed, the court added, § 3730(d) is referenced “at least six times,”1 but not once is “either the first-to-file rule or the public disclosure bar” so much as mentioned. This was telling, in the court’s view, because “the fact remains that the government did proceed with all seven of the underlying cases[,] .,. intervened in all, and settled each case,” and under a “straight forward reading of [§ 3730(d) ],” the Government’s conduct would entitle relators to attorneys’ fees.
After the district court ruled that CHS had failed to preserve its right to make first-to-file and public-disclosure challenges, CHS and the Tennessee Relators jointly moved for a stipulated award of $2,650,000 in fees, which the court granted. CHS then appealed.
II.
We review the district court’s interpretation of the settlement agreement de novo. See Orrand v. Scassa Asphalt, Inc., 794 F.3d 556, 560-61 (6th Cir. 2015). The settlement agreement provides that it is “governed by the laws of the United States'.” We thus “apply ‘general rules’ of contract law as part of the federal common law.” Cassidy v. Akzo Nobel Salt, Inc., 308 F.3d 613, 615 (6th Cir. 2002). “The federal common law may draw upon state law principles, but state law is not controlling authority.” Id.
“Where a contract’s meaning is clear on its face, that meaning controls.” In re Am-Trust Fin. Corp., 694 F.3d 741, 750 (6th Cir. 2012). To determine whether a contract’s meaning is clear on its face, we “consider the language of the agreement, the context in which that language appears and other traditional canons of construction.” Prater v. Ohio Educ. Ass’n, 505 F.3d 437, 441 (6th Cir. 2007); see also Gallo v. [414]*414Moen Inc., 813 F.3d 265, 273-74 (6th Cir. 2016) (“The first and best way to divine the intent of the parties is from the four corners of their contract and from traditional canons of contract interpretation.”). “If, after applying these rules of interpretation, the contract remains ambiguous,” then the parties’ original understanding of the contract’s terms may be ascertained through extrinsic evidence. Prater, 505 F.3d at 441. A contractual provision is ambiguous if it “is subject to two reasonable interpretations.” In re AmTrust Fin. Corp., 694 F.3d at 750 (citation omitted).
This appeal centers on Term 8 of the settlement agreement. The relevant sentence of Term 8 provides that “nothing in this paragraph or this Agreement shall be construed in any way to release, waive or otherwise affect the ability of CHS to challenge or object to Relators’ claims for attorneys’ fees, expenses, and costs pursuant to 31 U.S.C. § 3730(d).” CHS argues that this sentence preserves its ability to challenge or object to the relators’ claims for attorneys’ fees on any basis. Tennessee Relators contend that this sentence restricts CHS’s challenges and objections to those grounded in 31 U.S.C. § 3730(d). If both interpretations are reasonable, then Term 8 is ambiguous and the parties’ original understanding may . be ascertained by also considering extrinsic evidence.
A. Interpretation of CHS.
Two principles of contract interpretation, the last-antecedent presumption and the consistent-usage presumption, underlie CHS’s interpretation of Term 8. The last-antecedent presumption instructs that “a limiting clause or phrase ... should ordinarily be read as modifying only the noun or phrase that it immediately follows.” United States v. Hayes, 555 U.S. 415, 425, 129 S.Ct. 1079, 172 L.Ed.2d 816 (2009) (omissions in original) (quoting Barnhart v. Thomas, 540 U.S. 20, 26, 124 S.Ct. 376, 157 L.Ed.2d 333 (2003)); see also Lockhart v. United States, — U.S. -, 136 S.Ct. 958, 963, 194 L.Ed.2d 48 (2016) (observing that the Supreme Court “has applied the rule from our earliest decisions to our more recent”).2 The district court read the limiting phrase in Term 8—“pursuant to 31 U.S.C. § 3730(d)”—as applying to “the ability of CHS to challenge or object” to the attorneys’ fees. The last-antecedent presumption, CHS argues,' supports a reading that applies the limiting phrase to the phrase that immediately precedes it— “[rjelators’ claims for attorneys’ fees, expenses, and costs.” Accordingly, CHS concludes, the last-antecedent presumption supports its assértion that the settlement agreement preserves CHS’s right to challenge the relators’ claims for attorneys’ fees under the fírst-to-fíle and public disclosure rules.
CHS also relies on the consistent-usage presumption, which is the presumption that words and phrases have the same meaning throughout a contract. See U.S. Nat’l Bank of Or. v. Indep. Ins. Agents of Am., Inc., 508 U.S. 439, 460, 113 S.Ct. 2173, 124 L.Ed.2d 402 (1993) (applying the presumption of consistent usage to a statute); 11 Williston on Contracts § 32:6 (4th ed. 2015) (“Generally, a word used by the parties in one sense will be given the same [415]*415meaning throughout the contract in the absence of countervailing reasons.”); Thompson v. Amoco Oil Co., 903 F.2d 1118, 1121 (7th Cir. 1990) (applying Illinois law); McLane & McLane v. Prudential Ins. Co. of Am., 735 F.2d 1194, 1195-96 (9th Cir. 1984) (applying Arizona law). Here, the relevant phrase in Term 8 is “pursuant to 31 U.S.C. § 3730(d).” Two other provisions in the settlement agreement, Term 3 and Term 15(c)(1), also use this phrase after the phrase “claims Rela-tors may have for reasonable attorneys’ fees, expenses, and costs.” What distinguishes Term 3 and Term 15(c)(1) from Term 8, CHS argues, is the absence of other language to which the limiting phrase could attach; the only language to which the limiting phrase can attach in Term 3 and Term 15(c)(1) is “claims Rela-tors may have for reasonable attorneys’ fees, expenses, and costs.” Term 3 provides that “[a]ll Parties agree that nothing in this Paragraph or this Agreement shall be construed in any way to release ... any claims Relators may have for reasonable attorneys’ fees, expenses, and costs pursuant to 31 U.S.C. § 3730(d)....” Likewise, Term 15(c) provides
that the following claims shall not be dismissed, unless they are settled, adjudicated, or otherwise resolved, and any required consent by the United States is obtained, and the Courts are so informed: (1) Any claims Relators may have for reasonable attorneys’ fees, expenses, and costs pursuant to 31 U.S.C. § 3730(d)... ,3
Thus, CHS reasons, given that the limiting phrase must attach to “claims Relators may have for reasonable attorneys’ fees,' expenses, and costs” in Term 3 and Term 15(c)(1), the consistent-usage presumption supports a reading of Term 8 that attaches the limiting phrase to that language as well. That is to say, CHS’s reading.
B. Interpretation of the Tennessee Re-lators.
We now turn to the Tennessee Relators’ interpretation of the settlement agreement. Tennessee Relators read Term 8 as limiting CHS’s ability to challenge or object to relators’ claims for attorneys’ fees to arguments grounded in § 3730(d). They argue that the settlement agreement contains two indicia of meaning that support this interpretation.
First, Term 7 of the agreement explicitly states that the Government retains the ability “to contend that provisions in the False Claims Act, including 31 U.S.C. §§ 3730(d)(3) and 3730(e), bar Relators from sharing in the proceeds of [the] [a]greement.” In contrast, Term 8 does not explicitly state that CHS can challenge the relators’ claims for attorneys’ fees under the first-to-file rule set forth in § 3730(b)(5) or the public disclosure bar set forth in § 3730(e)(4). Tennessee Rela-tors argue that “when one party specifically reserves certain rights and another party does not, the natural, proper reading of that agreement is to conclude that the party that did not make its reservation explicit has in fact made no reservation at all.” Unlike the Government, CHS did not include the statutory references for the challenges it wished to preserve. Accordingly, Tennessee Relators contend, CHS’s failure to expressly preserve its right to challenge the relators’ claims for attorneys’ fees under § 3730(b)(5) and § 3730(e)(4) supports ■ reading the settlement agreement to limit CHS’s objections to those listed in § 3730(d).
The Tennessee Relators also point to Recital G. Recital G provides that “Rela-[416]*416tors and their counsel claim entitlement under 31 U.S.C. § 3730(d) ... to Relators’ reasonable expenses, attorneys’ fees and costs.” This expectation arises from § 3730(d), which requires the payment of reasonable attorneys’ fees whenever the Government proceeds with a qui tam action. Here, Tennessee Relators argue, the Government not only proceeded with the Tennessee Relators’ qui tam actions, but assigned their attorneys thousands of hours of work, yielding an $88 million recovery for the United States. Because CHS would agree to a settlement only if it included all seven relators, the Government asked the Tennessee Relators to dismiss their claims, suggesting that they reach a separate agreement with the other relators, which they did, for a portion of the proceeds. The Tennessee Relators infer from this that, in light of their contributions to the ease, they at least claimed that settlement would entitle them to attorneys’ fees.
The Tennessee Relators also refer to the contrast between Recital G and other recitals in the settlement agreement; for instance, Recitals C and D set forth the Government’s allegations regarding CHS’s conduct, and Recital F sets forth CHS’s denial of these allegations. By contrast, CHS does not set forth a counter-recital denying Recital G, which relators argue indicates tacit acceptance of the recital. It would be strange, however, for CHS to tacitly accept Recital G if it intended to raise first-to-file and public-disclosure challenges. Thus, Tennessee Relators conclude, CHS’s silence in response to Recital G supports an inference that it did not intend to raise such challenges.4
C. CHS’s responsive arguments.
CHS makes a number of arguments against Tennessee Relators’ interpretation of the settlement agreement. Even if the Tennessee Relators’ interpretation of Term 8 is correct, CHS argues, their interpretation of the agreement permits first-to-file challenges, and CHS is therefore permitted to make this challenge. We address these arguments separately.
1. Arguments related to Term 8.
CHS first argues that it is anomalous to interpret the reservation of rights in Term 8 as a waiver of rights! Earlier in Term 8, however, there is a broad waiver of rights, from which the last sentence of Term 8 is an exception. In pertinent part, Term 8 provides that
CHS ... fully and finally release[s], waive[s], and forever discharge^] each of the Relators ... from any and all manner of claims, controversies, actions, causes of actions, demands, torts, damages, costs, attorneys’ fees, moneys due on account, obligations, judgments or liabilities of any kind whatsoever in law or equity, arising out of agreement or imposed by statute, common law or otherwise, from the beginning of time to the date this Agreement is signed, whether or not known now, anticipated, unanticipated, suspected or claimed, fixed or contingent, whether yet accrued or not and whether damage has resulted from such or not. All Parties agree that nothing in this Paragraph or this Agreement shall be construed in any way to release, waive or otherwise affect the ability of CHS to challenge or object to Relators’ claims for attorneys’ fees, ex[417]*417penses, and costs pursuant to 31 U.S.C. § 3730(d).
The first sentence in Term 8 effectuates a broad waiver of CHS’s ability to raise “any and all manner of claims, controversies, actions, [and] causes of actions ... arising out of agreement or imposed by statute.” The second sentence in Term 8 then limits the scope of that waiver by providing that CHS reserves the right to “challenge or object to Relators’ claims for attorneys’ fees, expenses, and costs pursuant to 31 U.S.C. § 3730(d).” The Tennessee Relators claim entitlement to attorneys’ fees pursuant to § 3730(d) in Recital G of the settlement agreement. CHS’s attempts to challenge the Tennessee Relators’ entitlement to attorneys’ fees under the first-to-file and public disclosure rules are therefore “claims, controversies, actions, [or] causes of action” that “aris[e] out of agreement or [are] imposed by statute.” Accordingly, the first sentence in Term 8 operates to waive CHS’s ability to challenge the Tennessee Relators’ entitlement to attorneys’ fees under the first-to-file and public disclosure rules unless the second sentence in Term 8 preserves CHS’s ability to raise these challenges.
Second, CHS argues that Tennessee Re-lators’ interpretation is unreasonable because it “needlessly brings Term 8 into conflict with Term 15(c)(1).” Term 15(c)(1), CHS observes, says that “[a]ny claims Re-lators may have for reasonable attorneys’ fees, expenses, and costs pursuant to 31. U.S.C. § 3730(d)” shall not be dismissed “unless they are settled, adjudicated, or otherwise resolved.” CHS contends that this provision “contemplates that, even if a relator seeks reasonable fees, his or her claim may be challenged,” including with regard to “the issue of entitlement.” We disagree. A term that reserves a right to bring a claim and a term that circumscribes the types of challenges that may be brought against the claim are not mutually exclusive. Term 15(e)(1) simply excludes relators’ claims for attorneys’ fees from the set of claims being dismissed under the settlement agreement; it does not set forth the challenges available to CHS.
2. Arguments related to Recital G.
CHS' first argues that reliance on Recital G is “misplaced” because “many authorities hold that recitals cannot create legal obligations and are entitled to little weight in interpreting the operative provisions of a contract.” It is true that recitals “generally do not create binding obligations.” 17A C.J.S. Contracts § 403 (updated 2016). But recitals can establish “the background of a contract, that is, the purposes and motives of the parties.” 17A Am. Jur. 2d Contracts § 373 (updated 2016). They also “may have a material influence in construing the contract and determining the intent of the parties,” for if an operative section of a contract is ambiguous, “the recitals govern the construction.” Id.; see also 17A C.J.S. Contracts § 403 (observing that although recitals “do not control over the express provisions of a contract, they may be read in conjunction with the contract’s operative portions to ascertain the parties’ intention, where the operative clauses are ambiguous” (footnote omitted)); McKissick v. Yuen, 618 F.3d 1177, 1186 (10th Cir. 2010) (observing that recitals “may be looked to in determining the proper construction of the contract and the parties’ intention” (quoting Ferrell Constr. Co., Inc. v. Russell Creek Coal Co., 645 P.2d 1005, 1009 (Okla.1982))). Thus, even though Recital G does not itself create a binding obligation, it may guide interpretation of the binding obligation in Term 8, but only if that term is ambiguous in the first place.
CHS is correct that Recital G does not expressly bar CHS from challenging rela-tors’ entitlement to fees and, accordingly, does not render Term 8 unambiguous. But [418]*418CHS’s silence in response to Recital G still supports Tennessee Relators’ interpretation, even if it does not conclusively establish this interpretation. Had CHS intended to raise fírst-to-fíle and public-disclosure challenges, one might have expected CHS to deny Recital G and to record its belief that relators are not entitled to attorneys’ fees, just as relators’ recorded their belief that they are entitled to fees.
3. The impact of Tennessee Relators’ interpretation on fírst-to-fíle challenges.
CHS argues that even if the settlement agreement restricts its challenges and objections to those in § 3730(d), because § 3730(d) refers to § 3730(b)—for the purpose of identifying the FCA claim to which § 3730(d) applies (i.e., qui-tam claims rather than Attorney-General-initiated claims)—§ 3730(d) incorporates the fírst-to-fíle rule. We are unpersuaded. If the preserved fee challenges are restricted to the limits contained in § 3730(d), it would be anomalous to interpret that section to incorporate limits that engulf the restriction. Accordingly, if Tennessee Relators’ interpretation is correct, then CHS is precluded from making a first-to-file challenge.
D. Evaluation of the Parties’ Interpretations.
CHS and the Tennessee Relators have each advanced a reasonable interpretation of the settlement agreement. CHS’s interpretation is supported by the last-antecedent rule and the presumption of consistent usage. However, they are just that—presumptions—and, as the Supreme Court has observed with regard to the last-antecedent rule, “can assuredly be overcome by other indicia of meaning.” Hayes, 555 U.S. at 425, 129 S.Ct. 1079 (quoting Barnhart, 540 U.S. at 26, 124 S.Ct. 376). The Tennessee Relators have pointed to two “indicia of meaning” that support their interpretation: CHS’s failure to expressly preserve the fírst-to-fíle and public-disclosure challenges in Term 8, and CHS’s silence in response to Recital G. Term 8 is thus “subject to two reasonable interpretations,” rendering it ambiguous. In re AmTrust Fin. Corp., 694 F.3d at 750 (citation omitted).
Accordingly, extrinsic evidence may be used to ascertain the parties’ original understanding of its terms. Prater, 505 F.3d at 441. “It is not within [the panel’s] purview to resolve these ambiguities.” Lemley v. Ford Motor Co., 36 F.3d 1097 (6th Cir. 1994) (unpublished table decision) (per curiam), 1994 WL 483901 at *4. Where the district court holds that a contract is unambiguous and thus does not reach the extrinsic evidence, as here, remand is appropriate. See Sault Ste. Marie Tribe of Chippewa Indians v. Granholm, 475 F.3d 805, 816 (6th Cir. 2007) (observing that although “[t]he admissibility of extrinsic evidence is a question of law and is properly within [the court’s] province to determine ... [,] the amount of weight to accord extrinsic evidence is a question of fact and must be determined by a trier of fact”); Fed. Sav. & Loan Ins. Corp. v. Fed. Deposit Ins. Corp., 780 F.2d 1020 (6th Cir. 1985) (unpublished table opinion) (per curiam), 1985 WL 13960 (concluding that “the magistrate erred in failing to consider extrinsic evidence of such intent” and “remand[ing] for the consideration of such evidence”).
III.
For the foregoing reasons, we reverse the district court’s order and remand for proceedings consistent with this opinion.