Marge responded: “Some things will be dealt with at a later date.”

Lisa added, “If at all.”

Mr. Groening — whose name rhymes with “raining” — was one of the writers on the episode. After it aired, Al Jean, the showrunner since 1998, retweeted posts decrying political correctness.

But Hank Azaria, the Emmy-winning actor who voices “Apu,” told Stephen Colbert on “The Late Show” last week that he would be “perfectly willing and happy to step aside, or help transition it into something new.”

“The idea that anyone, young or old, past or present, was bullied or teased based on the character of Apu, it just really makes me sad,” he said. “It was certainly not my intention. I wanted to spread laughter and joy.”

Hoping to find a new story line for Apu, Adi Shankar, a producer and showrunner, announced a screenwriting contest on Monday. Mr. Shankar, who does not work for “The Simpsons,” asked for a script that takes Apu “and in a clever way subverts him, pivots him, intelligently writes him out, or evolves him in a way that takes a meanspirited mockery and transforms him into a kernel of truth wrapped in funny insight, a.k.a. actual satire.”

He pledged to deliver the winning script to the writers of “The Simpsons.” If they’re not interested, he would produce the script as “an unofficial fan film,” he said.

In an interview, Mr. Shankar said Apu was a “fabricated archetype, and it’s been carved into the American, and really the global, consciousness with blunt force.” The contest is intended to give “Simpsons” writers access to new perspectives in a way that would be a win-win, he said.