The Republican memo issued in February said the F.B.I. had failed to “disclose or reference the role of the D.N.C., Clinton campaign or any party/campaign in funding Steele’s efforts, even though the political origins of the Steele dossier were then known to senior D.O.J. and F.B.I. officials.” But Democrats at the time contended that the court had been told that the research had politically motivated origins.

The application contains a page-length explanation that does alert the court that the person who commissioned Mr. Steele’s research was “likely looking for information to discredit” Mr. Trump’s campaign. It goes on to explain why, notwithstanding Mr. Steele’s “reason for conducting the research,” the F.B.I. believed it was credible.

Republicans had also faulted the application for not explicitly identifying Mrs. Clinton’s campaign and the Democratic National Committee by name. But that criticism ignored the fact that law enforcement officials were following a general policy not to name Americans, even referring to Mr. Trump only as “Candidate #1” in renewal applications despite noting that he was now the president-elect and then the president.

David Kris, an expert on the Foreign Intelligence Surveillance Act who served in the George W. Bush and Obama administrations, dismissed the notion that the intelligence court judges had been misled.

“Now we can see that the footnote disclosing Steele’s possible bias takes up more than a full page in the applications, so there is literally no way the FISA Court could have missed it,” he wrote on the blog Lawfare. “The F.B.I. gave the court enough information to evaluate Steele’s credibility.”

Another issue in dispute was Republicans’ suggestion that a September 2016 Yahoo News article about Mr. Page’s ties to Russia was cited in the application as corroboration for Mr. Steele’s information even though it later emerged that he had been a source for that article. Democrats at the time said that was misleading because the purpose of including the article was instead to tell the court that Mr. Page had denied the allegations about his meetings in the July 2016 trip to Moscow.