DENNIS JACOBS, Circuit Judge:
Apple Inc. appeals from orders of the United States District Court for the Southern District of New York (Cote, J.), which imposed an external compliance monitor through a permanent injunction, allegedly modified that injunction to expand the role of the monitor, and denied Apple’s motion to disqualify the appointed monitor, Michael Bromwich. See United States v. Apple Inc., 992 F.Supp.2d 263 (S.D.N.Y.2014). In separate appeals that are not before this panel, Apple challenges the district court’s finding as to liability, and Apple and other defendants challenge the district court’s final judgment and permanent injunction. See United States v. Apple Inc., Nos. 13-3741, 13-3748, 13-3783, 133857, 13-3864, 13-3867. This opinion does not impact those appeals.
This appeal touches upon: the scope of a district court’s power under Federal Rule of Civil Procedure 53 to create and modify a monitorship over the objection of the monitored party; the professional and [134] structural constraints on that monitor’s activities; and the remedy available to the monitored party when it believes that the monitor has overreached. These largely procedural questions have considerable resonance because the fairness and integrity of the courts can be compromised by inadequate constraint on a monitor’s aggressive use of judicial power.
While some of Apple’s allegations against the monitor give pause, we are limited by both the record and our appel-' late jurisdiction. In view of those limitations, we review only (1) the district court’s denial of the motion to disqualify the appointed monitor, and (2) modifications of the injunction. We affirm, on the grounds that (1) on the record then before the district court, it did not abuse discretion in declining to disqualify the monitor, and (2) in light of this Court’s intervening interpretation of the injunction, the terms of the injunction are not currently affected by modifications (if any) made by the district court.
BACKGROUND
Following a bench trial, the district court found Apple liable for a violation of Section 1 of the Sherman Antitrust Act, 15 U.S.C. § 1. See United States v. Apple Inc., 952 F.Supp.2d 638 (S.D.N.Y.2013). Specifically, the district court found that five of the six largest e-book publishers in the United States had entered a horizontal “conspir[acy] with each other to eliminate retail price competition in order to raise e-book prices,” and that Apple, which was considering entry as a retailer, violated Section 1 by “facilitating and executing that conspiracy.” Id. at 647. (That ruling is currently on appeal before another panel of this Court.)
On September 5, 2013, the district court entered an omnibus order,, styled “Plaintiff United States’ Final Judgment and Plaintiff States’ Order Entering Permanent Injunction” (“the injunction”). Two sections of the injunction are relevant to this appeal: Apple is required to adopt policies and training to promote its compliance with the antitrust laws (Deferred Appendix (“D.A.”) 47274); and an external compliance monitor is to be appointed pursuant to Federal Rule of Civil Procedure 53, “to review and evaluate” Apple’s adoption of the required policies and training (D.A. 474-78). In addition, the injunction granted Apple leave to file with the district court written objections to the monitor’s conduct and to his recommendations, provided that Apple first raised these objections with the plaintiffs. (D.A. 476-77.)
The injunction specified that the plaintiffs (the U.S. Department of Justice, 31 states, the District of Columbia, and the Commonwealth of Puerto Rico) would recommend monitor candidates to the district court. Apple, meanwhile, was not permitted to recommend a candidate without the agreement of the plaintiffs (though Apple had an opportunity to object to the plaintiffs’ recommendations). The plaintiffs recommended Michael Bromwich as monitor, and the district court appointed him on October 16, 2013.
The relationship between Bromwich and Apple, which got off to a contentious start, raises three salient issues:
1. Apple argues that Bromwich opened inquiries prematurely. The injunction called upon the monitor to “assess whether Apple’s internal antitrust compliance policies and procedures, as they exist 90 days after his or her appointment, are reasonably designed to detect and prevent violations of the antitrust laws.” (D.A. 475.) Apple interpreted this provision as restricting Bromwich’s role during the first 90 days of his appointment (ie., until January 14, 2014), when the policies subject to [135] his scrutiny were yet to be formulated. Bromwich responded that he understood from his ex parte conversations with the district judge that he was “to get off to a fast start,” and that he gave that impression “far more weight than” the aspects of the district court record on which Apple relied. (D.A. 570.) Thus, Bromwich began his inquiries within six days after his appointment (four business days), requesting interviews with members of Apple’s Board of Directors. (D.A. 651 ¶ 17.)
He encountered push-back from Apple’s counsel as to the timing and scope of the inquiries, and by the sixteenth calendar day after his appointment, Bromwich began to accuse Apple of “failing] to provide any of the materials it had promised” and stalling in the scheduling of “brief preliminary interviews” with officers and directors. (D.A. 653 ¶ 27.)
2. The friction between Bromwich and Apple’s counsel prompted Bromwich to complain of foot-dragging, and induced him to write directly to Apple’s officers, proposing that they communicate with Bromwich directly, without the protection of counsel. Apple argues that the complaints were unfounded (especially given the 90-day period allowed for formulating the policy that Bromwich was to monitor) and that the effort to peel away counsel was improper for an agent of the court.
This is what happened. On November 1, 2013, Bromwich wrote a letter to Apple’s Chief Executive Officer, Timothy Cook, and to its Senior Vice President and General Counsel, D. Bruce Sewell, proposing “to establish a line of communication with the senior managers.” (D.A. 653 ¶ 26.) As Bromwich later explained, he wrote the letter because he already “had become concerned that the company was using its outside counsel as a shield.” (Id.) On November 22, Bromwich wrote directly to Cook and the members of Apple’s Board of Directors, decrying the “confrontational and obstructionist approach [Apple] has adopted in the first month of our relationship,” and urging them to “[p]romote a positive, direct relationship between the company liaisons and the monitoring team that is unfiltered through outside counsel.”' (D.A. 568.) The effort to exclude counsel continued as Bromwich began interviewing Apple’s directors: On December 5, Brom-wich told a director that his role as monitor required him to “crawl into a company” and that Apple must “take down barriers” to his access. (D.A. 832 ¶ 15.) He urged the same director to maintain direct contact with the monitorship team, referencing the fact that his past monitorships had not involved outside counsel at all. (Id.) As even the plaintiffs concede, Bromwich was expecting from Apple the level of submissiveness that he had found in past mon-itorship engagements, which had all resulted from consent decrees rather than from adverse judgments. Bromwich was thus unprepared for the formal and adversarial context of a monitorship imposed over the objection of the monitored party.1
[136]*1363. Apple also took issue with Brom-wich’s fees. The injunction requires Apple to pay the monitor’s fees “on such terms and conditions as [the plaintiffs] approve[].” (D.A. 478.) Thus the court-ordered fee paid to an agent of the court was effectively set by a plaintiff for payment by the defendant. Apple did not raise a specific objection to this arrangement when it was originally proposed. At the same time, the arrangement put considerable stress on the adversarial system, and consequences ensued.
Bromwich proposed to bill Apple $1,265 per hour ($1,100 plus a fifteen percent “administrative fee”). (D.A. 668.) He proposed lesser rates for other members of what he was assembling as his team, including $1,025 per hour for an antitrust lawyer to supply an expertise that the antitrust monitor lacked. (IcL)
In an exchange of letters in November 2013, Apple called the fee “unreasonable” and “non-customary.” (D.A. 577.) Brom-wich defended the reasonableness of the fee and disputed whether Apple had standing to register the objection in the first place: “the fees and expenses to be paid to the monitor and his team are not set by Apple; they are set by the monitor, with approval reserved for the DOJ and the Plaintiff States.” (D.A. 573.) Within the first two weeks after his appointment, Bromwich had billed $138,432.40, fueling Apple’s allegation that Bromwich had jumped the gun to maximize a commercial opportunity. (D.A. 579.)
These disputes culminated in a series of filings in the period November 2013 through January 2014. The district court proposed on November 20 to amend the injunction by, among other things, providing for ex parte briefings between the monitor and the district judge at least once a month. (D.A. 485.) Apple objected, and raised some additional objections related to the monitorship, including: that the court lacked jurisdiction to modify the injunction while Apple’s appeal of the final judgment was pending; that the proposed modifications exceeded the district court’s appointment power under Rule 53; that the proposed modifications would contravene the constitutional separation of powers by allowing ex parte communications between Bromwich and the plaintiffs at the same time as allowing ex parte communications between Bromwich and the district court; that the district court should not receive ex parte communications from Bromwich while it continued to preside over related antitrust litigation against Apple; that Bromwich’s fees were excessive, perverted Bromwich’s incentives, and deprived Apple of a disinterested monitor; and that Bromwich had exceeded the authority he was given in the injunction.
Following Apple’s objections, the district court agreed to forgo ex parte communications with the monitor. As to Apple’s other grievances, the district court generally “note[d] that ... the Injunction provides that the Monitor shall serve on such terms and conditions as the Department of Justice, after consultation with the Plaintiff States, approves” and explained that “[t]he Monitor’s compensation is to be on reasonable and customary terms.” (D.A. 520.) The district court also reminded Apple that it had available a process for objecting to the monitor’s actions, namely filing written objections with the court after consultation with the plaintiffs.
On December 14, 2013, Apple moved the district court by order to show cause for a stay of the injunction pending appeal. The plaintiffs’ opposition papers cited a decla[137] ration of Bromwich, which was — simultaneously — filed with the court by the plaintiffs. (D.A. 68, 626, 647.) Apple then requested that the district court disqualify Bromwich from serving as monitor, based on what Apple called “[h]is wholly inappropriate declaration in an adversarial proceeding.” (D.A. 798.) On January 16, 2014, the district court denied both the stay motion and the disqualification motion. See United States v. Apple Inc., 992 F.Supp.2d 263 (S.D.N.Y.2014). In doing so, however, the district court attempted to resolve some of Apple’s underlying grievances, such as by noting that the injunction explicitly “permits Apple officers, employees or agents to have ‘counsel present’ during any interviews.” Id. at 287.
This appeal followed. Apple’s Notice of Appeal explains its intention to challenge the January 16 order as well as modifications to the injunction.
The present appeal was the predicate for Apple’s motion in this Court for a stay pending appeal. A prior panel denied the stay on February 10, 2014, relying on concessions that the plaintiffs had made in connection with the stay motion. The plaintiffs had “explicitly stated that the district court’s order should be interpreted narrowly.” (Motion Order, Feb. 10, 2014, at 2.) No stay was deemed necessary because there was (by then) no dispute that the extent of the monitor’s responsibility is “to assess the appropriateness of the compliance programs adopted by Apple and the means used to communicate those programs to its personnel,” and “that the injunction would not allow the monitor to investigate whether such personnel were in fact complying with the antitrust or other laws.” (Id.) Accordingly, “the monitor was empowered to demand only documents relevant to his authorized responsibility as so defined, and to interview Apple directors, officers, and employees only on subjects relevant to that responsibility.” (Id.)
The panel relied on that narrow interpretation of the injunction, “tak[ing] [plaintiffs’] counsel’s statement as a formal representation that [plaintiffs] also accept that interpretation, and that the monitor will conduct his activities within the bounds” so delimited. (Id.) This narrow interpretation of the injunction is now the law of the case.
Apple also moved this Court to supplement the appellate record with documents concerning the monitor’s activities, including his billing records. This one-judge motion was denied.
DISCUSSION
Consideration of this appeal is circumscribed by our limited jurisdiction. “In cases involving a protracted remedial phase,” we may review “substantive post-judgment orders.” United States v. Yonkers Bd. of Educ., 946 F.2d 180, 183 (2d Cir.1991) (per curiam) (citing Firestone Tire & Rubber Co. v. Risjord, 449 U.S. 368, 373-74, 101 S.Ct. 669, 66 L.Ed.2d 571 (1981); Milliken v. Bradley, 433 U.S. 267, 97 S.Ct. 2749, 53 L.Ed.2d 745 (1977)). We also have jurisdiction over “[interlocutory orders ... continuing, modifying, refusing or dissolving injunctions, or refusing to dissolve or modify injunctions.” 28 U.S.C. § 1292(a)(1). However, when the challenge is to an implicit (rather than explicit) modification, we have jurisdiction only “[i]f we conclude that such a modification has occurred, and that the order of the district court ‘might have a serious, perhaps irreparable, consequence.’ ” EEOC v. Local 40, Int'l Ass’n of Bridge, Structural & Ornamental Iron Workers, 76 F.3d 76, 80 (2d Cir.1996) (quoting Carson v. Am. Brands, Inc., 450 U.S. 79, 84, 101 S.Ct. 993, 67 L.Ed.2d 59 (1981)). We therefore have [138] appellate jurisdiction to review: (I) the denial of Apple’s motion to disqualify Michael Bromwich as monitor; and (II) any implicit modification of the injunction having serious consequences. The Notice of Appeal that gave rise to this appeal expressed Apple’s intent to challenge only the rulings in the district court’s January 16, 2014 order and modifications to the injunction; so we lack jurisdiction in this appeal to review the facial legality of the injunction as it was entered by the district court. See New Phone Co. v. City of New York, 498 F.3d 127, 130 (2d Cir.2007) (“[O]ur jurisdiction is limited by the wording of the notice [of appeal].”).
I
As an appointee of the court pursuant to Rule 53, the monitor is subject to the same grounds for disqualification as “would require disqualification of a judge under 28 U.S.C. § 455.” Fed.R.Civ.P. 53(a)(2). Disqualification is necessary when (among other situations) “his impartiality might reasonably be questioned,” 28 U.S.C. § 455(a); “he has a personal bias or prejudice,” id. § 455(b)(1); or he “has a financial interest in the subject matter in controversy,” id. § 455(b)(4).
A district court’s denial of a motion to disqualify is reviewed for abuse of discretion. In re Basciano, 542 F.3d 950, 956 (2d Cir.2008). Given this deferential standard, and the limited record before the district court at the time it denied Apple’s motion to disqualify Bromwich, we cannot conclude that the denial was error.
A
Apple’s principal arguments for Bromwich’s disqualification are based on his ex parte communications and collaboration with the plaintiffs.2 The record reflects one significant instance of such collaboration: Bromwich coordinated with the plaintiffs in their opposition to Apple’s stay motion in the district court, and submitted an affidavit as an integral part of the opposition papers. The plaintiffs’ brief in opposition, filed on the same day as the declaration, cites to it. The district court found that the declaration was Bromwich’s opportunity to respond after Apple made factual assertions that were critical of Bromwich’s work, and was not evidence of bias or prejudice against Apple.
It is certainly remarkable that an arm of the court would litigate on the side of a party in connection with an application to the court he serves. The commentary on Rule 53 discourages any ex parte communication between a court appointee and a party, noting that “[i]n most settings, ... ex parte communications with the parties should be discouraged or prohibited” by the district court. Fed.R.Civ.P. 53(b) advisory committee’s notes to the 2003 amendment. Moreover, Bromwich’s submission in conjunction with a litigant’s brief was the opposite of best practice for a court-appointed monitor. A judicial officer should prefer to file documents independently when such an option is available, and not through one party or another. Nevertheless, our concerns regarding Bromwich’s declaration are procedural rather than substantive. Apple does not argue that a problem would have arisen if he had filed the same declaration either on [139] his own behalf or at the invitation of the district court and without coordinating with the plaintiffs.
The manner in which the declaration was filed, and the fact that it was preceded by at least some ex parte communications with the plaintiffs, however, may raise “an appearance of partiality” and “an appearance of impropriety,” Liljeberg v. Health Serv. Acquisition Corp., 486 U.S. 847, 860-61, 108 S.Ct. 2194, 100 L.Ed.2d 855 (1988). At the same time, Rule 53 expressly contemplates the possibility of ex parte communications with a monitor; and here, the injunction itself (the propriety of which we do not review in this appeal) contemplates at least some interaction between the monitor and the plaintiffs (for example, in the setting of the monitor’s fee, a subject bound to be of considerable interest to the monitor). Still, the evidence of ex parte communication before the district court is limited on this appeal to Bromwich’s filing of his declaration, and the plaintiffs’ citation to it. On this record, we cannot say that the district court abused its discretion when it concluded that the declaration did not require Bromwich’s disqualification.
Apple intimates that Bromwich engaged in additional ex parte communications with the plaintiffs — communications that “cul-minat[ed]” in Bromwich’s declaration and the plaintiffs’ opposition papers. (Appellant’s Opening Br. at 9.) But such communications are not evident in the record on this appeal.3 Our present ruling is therefore without prejudice to any further applications to the district court, informed by évidence not in the present appellate rec,ord.
B
Apple further contends that Bromwich should be disqualified because his hourly fee creates a corrupting incentive inconsistent with 28 U.S.C. § 455(b)(4). Underlying this contention is Apple’s assertion that the amount of Bromwich’s fee — now cut-rate at $1,000 per hour4 — is excessive.
We do not understand the ground of Apple’s complaint to be hardship. Rather, the fee is integral to Apple’s other objections.
• The monitor’s ex parte contacts with the plaintiffs were to an extent contemplated by the injunction itself, which sent the monitor to negotiate his fee with Apple’s adversaries (which had nominated him). ' There is an ineluctable rapport between a lawyer and a generous client.
• The hourly rate could be (and is) seen by Apple as an incentive to jump the gun by initiating inquiry before the 90-day period had elapsed, to pile on with interviews and demands, to clear [140] obstacles from Apple’s counsel, to dilate the role of the monitorship, and to prolong its life.
• These perceptions (the findings are not for us to make) place Apple in the position of either tolerating the monitor’s conduct (including interference with counsel) or registering complaints that threaten the financial expectation of an agent acting for a powerful court. This was a machine for making conflict, hostility and unhealthy appearances.
The fee dispute is thus rooted in the terms and operation of an injunction that we lack jurisdiction to review on this appeal.
While fees bespeak financial interest, and therefore should have been disclosed from the outset, the existence of a financial interest is not determined by the hourly billing rate, rich as it may be. Accordingly, our review of the district court’s denial of disqualification does not weigh the amount of Apple’s payments to Bromwich. Any monjtor would be entitled under the terms of the injunction to receive reasonable compensation. Therefore, neither the fact of Bromwich’s ongoing compensation nor the accumulating total of that compensation distinguishes him from any other potential monitor. The district court did not abuse discretion in declining to disqualify him on a basis that would apply to any monitor that might replace him.
C
At oral argument, both sides discussed more recent interactions that were not before the district court when it denied the disqualification motion. Given our jurisdiction, the standard of review, and the present appellate record, we cannot consider whether those interactions would justify or compel disqualification. Based on the record available to the district court at the time of its decision, there was no error in its denial of the disqualification motion.
II
In the district court and here, Apple has attacked much of Bromwich’s conduct as extending beyond the terms of the injunction, including: ex -parte collaboration with the plaintiffs; an overly aggressive “non-judicial investigation]” exceeding the purview of the monitorship; demands for interviews with Apple executives and directors unrelated to the antitrust compliance program; assertion of authority to review Apple’s “ ‘tone’ and ‘culture’ ”; and attempts to circumvent counsel retained by Apple to represent it in this case. (D.A. 798-99.) According to Apple, the district court constructively expanded the injunction to countenance this conduct, by denying Apple’s motions that were predicated on these objections.
The parties sharply dispute whether the injunction was ever modified, but for all practical purposes this issue is now moot: regardless whether the monitor’s conduct and the district court’s acquiescence modified the injunction, this Court subsequently construed the injunction (as it existed in February 2014, the time of the motion order) to impose sharp limits on the monitor’s power. The injunction is now defined by those limits, obviating modifications (if any) that broadened the injunction beyond those limits.
Moreover, notwithstanding the terms of the injunction, the monitor’s conduct is limited by other provisions of law and notions of professionalism. Checks on the monitor’s conduct include the statutory restrictions of 28 U.S.C. § 455 and the ethical limitations of the Code of Conduct for United States Judges.5 The monitor is [141] therefore subject to prohibitions against improper ex parte communications as well as “other communications concerning a pending or impending matter that are made outside the presence of the parties or their lawyers.” Code of Conduct for United States Judges, Canon 3(A)(4). Bromwich is also subject to his professional responsibilities: as a lawyer, he is bound to respect the role of counsel and the adversarial system; as an impartial arm of the court, his responsibility to those institutions is a public trust. These manifold checks reassure us that, notwithstanding any supposed acquiescence by the district court, the monitor is prohibited from trampling rights of counsel and adversarial principles.
In short, the injunction that presently applies to the parties and the monitor does not permit the troubling consequences that Apple fears the injunction was modified to allow. Further, to the extent that Apple objects to any future actions of the monitor, it may avail itself of the district court’s dispute resolution procedure and, if appropriate, seek judicial relief. Accordingly, the injunction has been neither substantially nor consequentially modified, see EEOC v. Local 40, Int’l Ass’n of Bridge, Structural & Ornamental Iron Workers, 76 F.3d 76, 80 (2d Cir.1996), and the monitor’s conduct remains appropriately constrained by the injunction and by other powerful restraints of law.
CONCLUSION
For the foregoing reasons, we hereby AFFIRM the decisions of the district court, without prejudice. The letter of the U.S. Department of Justice dated March 12, 2015, disclosing the fee schedule, is hereby ordered UNSEALED and the Clerk of Court is directed to make that letter publicly available on the’ docket.