Lisa D. Cook on Wednesday fought back against President Trump’s latest attempt to try to oust her from her role at the Federal Reserve. In a defiant reply, a lawyer for Ms. Cook stressed that she had committed no crime, nor had been charged with one, even as Mr. Trump had forged ahead with an attempt to dismiss her from the central bank over unproven allegations of mortgage fraud. Ms. Cook, a Fed governor, and her lawyer submitted the formal filing in response to a letter from the White House, which renewed its attempts to fire Ms. Cook this month. Mr. Trump had tried, and failed, to fire her in a process that began last year, until the Supreme Court halted it, finding that the president did not afford her an ample opportunity to respond to the charges.

The Trump administration’s allegations against Ms. Cook hinge on her 2021 purchase of a condominium in Atlanta, which she listed as a “primary” residence in at least one mortgage document, despite never living there. Ms. Cook also maintained another home in Ann Arbor, Mich., which was also designated as a “primary” residence. In his letter, Ms. Cook’s lawyer, Abbe David Lowell, said listing the Atlanta condo as a primary residence was an “entirely inadvertent oversight,” not fraud. He noted that Ms. Cook had correctly identified the property as a vacation home earlier in the mortgage application process, and said she had not received a preferential rate on her loan as a result of the error. Ms. Cook had not yet been nominated to the Fed board at the time of the purchase. Mr. Lowell also sought to argue that Mr. Trump and some of his other advisers had made similar designations on their own mortgage documents, citing public reporting.

For one example, Mr. Lowell pointed to a report from Bloomberg indicating that Scott Bessent, the Treasury secretary, had acquired mortgages on two homes in 2007 that had been designated as “primary” residences.