The comment came at a sensitive time for Donald J. Trump’s presidential campaign. Several members of his Hispanic advisory council withdrew their support this week, saying they had been led to believe that Mr. Trump was shifting his hard-line tone on immigration.

“He used us as props,” said Jacob Monty, who resigned after Mr. Trump reverted to his fiery language on immigration Wednesday night after returning from Mexico, where he had struck a more measured, even subdued, tone.

During the interview with Mr. Gutierrez, Ms. Reid quickly interjected, saying, “I don’t even know what that means, and I’m almost afraid to ask.”