In May, the Biden administration extended temporary protected status for 150,000 Haitians already living in the United States. Two months later, the order was extended again for Haitians in the United States before July 29. But tens of thousands more Haitians have attempted to cross into the United States since then, despite not qualifying for the program.The Biden administration, facing the highest level of border crossings in decades, has enforced policies intended to slow their entry.“We are very concerned that Haitians who are taking this irregular migration path are receiving false information that the border is open or that temporary protected status is available,” Alejandro N. Mayorkas, the secretary of the Department of Homeland Security, told reporters on Monday in Del Rio. “I want to make sure that it is known that this is not the way to come to the United States.”Still, thousands of Haitian migrants have been allowed to enter the country and will wait for their cases to go through the backlogged immigration court system.For the most part, officials are only deporting single people. Families with young children and pregnant women, for example, are typically being allowed in and released, in some cases with a monitoring device, according to officials familiar with the operations who spoke on condition of anonymity because they were not allowed to speak publicly about the matter.Mr. Foote was said to have pushed for greater oversight and responsibilities in his job as envoy to Haiti, efforts that were rejected by senior State Department officials. The department’s spokesman, Ned Price, on Thursday said some proposals put forward, including by Mr. Foote, “were determined to be harmful to our commitment to the promotion of democracy in Haiti and were rejected during the policy process.”“No ideas are ignored, but not all ideas are good ideas,” Mr. Price said. He was responding to Mr. Foote’s claim, in his resignation letter, that his recommendations were “ignored and dismissed.”