"Now you're still married to your former husband Kris Humphries?... When are you going to wrap that up?," he asked her.
Kim laughed and explained that she's been trying "to, um, wrap it up" for the past two years, but that it's a process and it's been hard. Adding that all she wants is for Humphries to be happy and for the two of them to move on.
"When the divorce comes through, and he wants an annulment, is that right? Why an annulment, what's the difference?" Letterman insisted, prompting the star to reveal that she's being sued by her husband.
"I don't really know cause even if we got an annulment... the only legal way to get an annulment is if fraud were involved, so that's what tricky. So he is suing me for an annulment based on the fact that I frauded him into marrying him for publicity, " she said.
When the host probed Kim on the validity of her marriage, it was her sister who answered.
"I think if she was going to do it for publicity, she'd pick someone that people knew," Kourtney said.