Letterman told the story Monday when prompted by "Late Show" guest James Franco, the star of Korine's latest film, "Spring Breakers."
Franco said he heard Korine was banned from the show after he pushed Streep backstage.
"He said he was a little out of it," Franco said of the "Kids" writer and "Gummo" writer-director.
"Harmony is a very sane guy now -- a great artist and great person to work with. But I think he had a period where he was going a little off the rails, so maybe he was on something that night," Franco said.
"I went upstairs to greet Meryl Streep and welcome her to the show, and I knock on the door ... and she was not in there," Letterman said of the last time Korine visited the "Late Show" studio in the late 1990s. "And I looked around, and she was not in there, and I found Harmony going through her purse. True story. And so I said: 'That's it. Put her things back in her bag and then get out.'"
"So, you kicked him off?" Franco asked Letterman, to which the talk-show host nodded emphatically as the studio audience applauded.
Apparently convinced by Franco's assertion that Korine is now a changed man, Letterman said he would be "more than happy" to have him back as a guest.