From an interview with Richard Kelly (writer/director of Donnie Darko):
Can you explain the character of Cherita [Chen]?
I like to call her my ‘Mike Yanagita.’ Remember Mike Yanagita from “Fargo?” He hits on Frances McDormand at the Radisson. They have Diet Cokes at the Radisson and he comes on to her.
If the Coen Bros. didn’t have final cut, a studio executive would have demanded that they cut that scene because it doesn’t make sense, it doesn’t contribute to the plot. But if you really pay attention to “Fargo,” that scene is really pivotal to Frances McDormand’s character because when she finds out that Mike Yanagita is completely lying about his wife dying, that it was a complete lie, she’s just shocked that she could have been lied to. She’s such a trustworthy person and it makes her go back to William H. Macy’s car lot to question him again.
So the Mike Yanagita scene is actually really, really important on a character level. On a plot level, it’s superfluous and it’s just the Coen Bros. just being weird or self-indulgent maybe. But I think it’s a great pivotal scene for character reasons and I think that’s probably what they thought, too.
Using that metaphor for Cherita Chen, she contributes nothing to the plot at all. She is extraneous and superfluous, but that moment where Donnie is wearing the earmuffs couldn’t exist were it not for Cherita Chen. That is a very important character moment.
From an interview with Frances McDormand:
[The Coen Bros.] told me they wanted to develop Marge’s character in a different context, other than with her husband, or with the murder case. Any character development—that’s good. So when they come up with this Mike Yanagita scene—I didn’t really get it until I saw the finished movie.
In that scene with Mike Yanagita, she realized he was lying. That’s the biggest thing she has to accept, because at the end when she talks about greed and not understanding why these guys did what they did, that’s just Marge’s general condition.