BURBANK, Calif. — The television producer Lisa Gregorisch-Dempsey is known for her terrifying candor. The nameplate on her desk at Telepictures, where she has run the celebrity news show “Extra” for 19 years, sums up her style: “I’ll be nicer if you’ll be smarter.” But even her longtime lieutenants were a bit startled by the way she laid it on the line for Billy Bush when she interviewed him for a job last year.

“I looked him in the eye and said, ‘I don’t know if you have enough humility for people to welcome you back,’” Ms. Gregorisch-Dempsey recalled. “America loves a comeback story. But we have to like you for America to like you.”

Ms. Gregorisch-Dempsey was overhauling “Extra” at the time and needed a new anchor. She had given Mr. Bush his TV start in 2001, when he briefly worked as an “Extra” freelancer. But he had been out of television work since fall 2016, when a leaked audio recording from “Access Hollywood” showed him laughing as Donald J. Trump bragged about grabbing women “by the pussy.”

Mr. Bush was widely criticized for his role in the misogynistic off-camera conversation, which had taken place in 2005. He swiftly lost the plum job he had landed earlier in 2016 as a 9 a.m. host of NBC’s “Today” show.