Mr. Rushing told the woman it was because of budgetary constraints, but she asserts in the complaint that Ms. Jackson Lee was conspiring with the foundation to retaliate after speaking with Ms. Washington, the foundation’s chief executive, about what had transpired at the foundation. She claims the firing has caused emotional, financial and career damage.But the foundation official said that Ms. Washington, who has since left her position there for unrelated reasons, denied asking for the woman to be fired or punished. On the contrary, the official said, she reached out by text with the intention of simply telling Ms. Jackson Lee that her employee was a former Congressional Black Caucus Foundation intern. The two never actually spoke, the official said.Ms. Bernabei, the woman’s lawyer, defended her client: “The justifications they have provided along the way, they are not credible, and they are shifting,” Ms. Bernabei said in an interview.In a statement, the foundation pledged to cooperate fully with an investigation of the claims.“We are deeply concerned about the welfare of all our interns and fellows, including ‘Jane Doe,’ the former C.B.C.F. intern who recently filed suit,” said C. J. Epps, a spokesman. “It is C.B.C.F.’s position that the foundation did not have the purview to terminate Ms. Doe from a staff position in a congressional office, and therefore, did not take such action nor recommend or influence said decision.”Still, the foundation’s board, which counts several high-profile corporate executives and members of Congress among its members, began moving last week to remove Ms. Jackson Lee, as first reported by Politico. Ultimately, the members decided to try to afford her a graceful exit and warned her late last week that if she did not step down, they would be forced to vote to remove her.On Wednesday, Elsie L. Scott, the foundation’s interim chief executive, thanked Ms. Jackson Lee for her leadership and the “longstanding commitment to inspire young people to become involved in their communities and government.” She said the congresswoman had made clear to the foundation that she “does not want to be a distraction during the legal proceedings.”When the Judiciary Committee met Wednesday morning to vote on subcommittee chairmanships and make other organizational decisions, Ms. Jackson Lee preemptively offered up an arrangement to give up the chairmanship she was in line for while the case proceeds, Democrats in the room said. Representative Karen Bass, Democrat of California and the chairwoman of the Congressional Black Caucus, will fill the subcommittee slot in the meantime.