Well in part what Simon said, they haven’t really shown WHY she is in that top secret, top scientific research ship in the first place (I mean her qualifications) other than to be the “comedic” relief. Also, they’re at war, you’d expect a war vessel to be outfitted with people at least some military training, which she doesn’t. She’s really a character that seems forced in just for comedy’s sake, and unfortunately, the comedy doesn’t even work for me. Her only merit so far has been to be assigned to the same room as Michael.
Other than that, her character is really a late 90’s early 2000’s prototypical “whedon-like” sidekick, she’d fit right in a show like Firefly or the Orville from what I saw, for sure, but I don’t feel she fits here, since this seems to be a “serious” show.
In contrast, for exemple, the Doctor is also super quirky, but he is immediatly introduced as this super genius and he shows his skills right away, so his quirkiness is excusable at least. Plus he’s nowhere near as annoying or “immersion-breaking” as Tilly… So yeah, I’d say the fact that she’s flat-out a comedy relief character is what REALLY bothers me, because she takes me out of the show everytime she opens her mouth… I’m always like “how the fuck did she even make it aboard???”