It's not a mistake because she's a prostitute!
Oh, just kidding. She was nothing of the sort. She was Millie's RIVAL. The concept of having a “Rival” is on the wane, it seems; people have “frenemies,” to use the awful word. If they’re in a workplace situation there would be non-judgmental counseling to help everyone move forward. But this is the fashion world of the early 70s, an era of cocaine and promiscuity, so everyone’s ready to claw each other’s eyes out.
Several questions: if the MEN’S GRILL is a men-only restaurant, it would be a private establishment, and hence would not need a sign. Second: if the men are so anxious for the sight of a woman at lunch, why would they join a men-only grill? Third: we were always supposed to like Millie in the Marvel world, because she was decent and kind and spunky, but Chili was the one you’d want to hang out with. Vain, yes, but for good reason.