The president has said repeatedly that diversity, equity and inclusion policies in hiring are illegal and discriminatory and that he intends to get rid of them. The federal Equal Employment Opportunity Commission, in what has been seen as a related move, sent letters to 20 law firms last month requesting information about their D.E.I. practices. Four of the firms that reached deals with Mr. Trump — Kirkland, Latham, Shearman and Simpson Thacher — had each received one of those letters. In settling, Mr. Trump said the E.E.O.C. had agreed not to pursue claims against those four firms. Later in the day, the E.E.O.C. announced a separate settlement with the four firms. Law professors and others in the legal industry have praised the firms that are fighting the administration while criticizing those that have settled. The critics say the law firms that settle have succumbed to pressure tactics by the administration. And each new settlement only encourages Mr. Trump to become even more emboldened in his demands for free legal work. The Trump administration seems to believe it is “developing a war chest of legal enlistees or conscripts” to do work for it, said Harold Hongju Koh, a professor of international law at Yale Law School, who was an author on a recently published paper that called the executive orders unconstitutional retaliatory measures. “Every kid learns, on the schoolyard, if you cave to a bully they will come back to bully you some more,” said Mr. Koh.