Apple Inc.’s court-appointed antitrust monitor, Michael Bromwich, reports that after a rough start, he and Apple are getting along better now. But Apple still wants him gone, as the tech giant made clear on May 1 in an appellate brief seeking Bromwich’s removal.

Apple’s lawyers at Gibson, Dunn & Crutcher asked the U.S. Court of Appeals for the Second Circuit to reverse portions of the final judgment in the e-books price-fixing litigation that led to Bromwich’s appointment. Asserting that his appointment was unconstitutional and unprecedented, they also took aim at Bromwich’s fees, complaining that his company billed Apple more than $1 million for less than six months of work.

After a bench trial that pitted the U.S. Department of Justice against Apple, U.S. District Judge Denise Cote in Manhattan ruled last July that Apple fixed e-book prices. Four months later, Cote appointed Bromwich to oversee Apple’s antitrust compliance programs. A partner at Goodwin Procter, Bromwich is billing Apple through his Washington, D.C.–based consulting firm, the Bromwich Group.

In late 2013 Apple unsuccessfully pleaded with Cote to remove Bromwich, arguing that Bromwich had gone beyond his assigned role by “interrogating Apple personnel about matters unrelated to the injunction in an effort to ferret out any wrongdoing.” After Cote refused to remove Bromwich, Apple appealed. In February the Second Circuit denied Apple’s request for a stay to halt Bromwich’s work, but gave Apple cause for hope by opining that Bromwich’s current role is simply to “assess the appropriateness of the compliance programs adopted by Apple and the means used to communicate those programs to its personnel.”

Apple included Bromwich’s monthly invoices with its May 1 brief. The tab for March alone came to about $271,000 in fees and costs, including $136,000 charged by Fried, Frank, Harris, Shriver & Jacobson partner Bernard Nigro Jr., who is assisting Bromwich. Apple is clearly hoping that the invoices will bolster its contention that Bromwich has a financial incentive to ignore limits on his role.

At press time the Justice Department had not responded to Apple’s May 1 brief. The government lawyer leading the case, Lawrence Buterman, has argued that Bromwich’s conduct has been “wholly within the scope of his authority” and “consistent with his impeccable reputation.”

In an April 14 report, Bromwich called the battle over his appointment regrettable and avoidable, but said there has been a “shift of tone” in his dealings with Apple since February. He attributes it in part to Apple’s designation of Simpson Thacher & Bartlett as the outside counsel with whom he deals, rather than Gibson Dunn.

A Bromwich Group spokesperson declined to comment. Apple lead appellate counsel Theodore Boutrous Jr. of Gibson Dunn also declined to comment.