In a six-page letter to Mr. Nadler on Thursday, her lawyers, Robert P. Trout and Gloria B. Solomon, wrote that despite the proximity of the calls to negotiations Mr. Cohen was conducting on silencing the women, the communications in question were not about the payments. They also noted that federal prosecutors involved in the case had never taken issue with her testimony.

[Read the letter from Ms. Hicks’s lawyers.]

“In sum, the information in the search warrant affidavit is not inconsistent with Ms. Hicks’s testimony, and does not establish any lack of candor on her part,” the lawyers wrote. “Ms. Hicks took her obligations seriously when she was interviewed by the committee. Her testimony was consistent with her previous statements on these issues and was truthful to the best of her knowledge and recollection.”

A spokeswoman for committee Democrats said they would review the letter to determine what steps to take.

Democrats want to explore other areas of investigation with Mr. Lewandowski and Mr. Dearborn, including their knowledge of the Trump campaign’s contacts with Russians and its views of Russia’s efforts to interfere in the race on its behalf. But their principal interest revolves around their knowledge of meetings Mr. Lewandowski had with Mr. Trump in June and July 2017, shortly after he directed his White House counsel, Donald F. McGahn II, to fire Mr. Mueller, an order Mr. McGahn rebuffed.

In his conversation with Mr. Lewandowski, the president “dictated a message” he wanted Mr. Lewandowski to deliver to Mr. Sessions, according to Mr. Mueller’s report. The message instructed Mr. Sessions, who was recused from the matter, to declare the special counsel’s investigation “very unfair” to the president and then curtail its scope to preventing future interference, effectively ending the scrutiny of Mr. Trump’s campaign.

Mr. Trump asked Mr. Lewandowski about the status of the message again a month later, and his former campaign manager advised him that he would deliver it soon. Hours afterward, the president criticized his attorney general in an interview with The New York Times.

Mr. Lewandowski never delivered the message directly to Mr. Sessions, asking Mr. Dearborn, a former Sessions aide, to do so instead. Mr. Mueller wrote in his report that Mr. Dearborn was uneasy about the request himself and also never delivered it.