“I applaud it,” Mr. Eisen said Wednesday. “I do think there has been a baptism of fire for all of the members of the Trump family, and there are some signs that they are responding appropriately to criticism.”

Added Mr. Painter: “I don’t think President Trump or the children are really used to the idea that he will be president and the public scrutiny that results. They are realizing it now.”

But Mr. Eisen and Mr. Painter said the Trump family must still resolve major outstanding conflicts involving the president-elect’s business operations — and ensure that the children of Mr. Trump who will be running his business no longer participate in any government-related meetings. Eric Trump has returned full time in recent weeks to the Trump Organization, which he intends to help run after his father enters the White House.

“Now they have to resolve the big issue: The father has to divorce himself from his conflict by appointing an independent trustee for his businesses,” Mr. Eisen said. Mr. Trump recently postponed a news conference during which he was supposed to address the concerns about the businesses.

The auction for coffee with Ms. Trump was terminated on Friday, after The Times reported that several of the highest bidders had said in interviews that they had entered the competition in hopes of using her as a way to get a message to her father on issues such as immigration and election fraud.

In addition, Eric Trump and his brother Donald have now said they will no longer participate in the post-inauguration charitable hunting trip. Details about the charity behind the event were first reported by the Center for Public Integrity, a nonprofit journalism outfit.

But Eric Trump went further on Wednesday evening, saying he realized his fund-raising could cause his family problems while his father is in the White House.