She had a bad tooth pulled.

Literal

She [topic-は] bad tooth [object-を] extract [received-the-favor-てもらった].

歯を抜いてもらう ('have a tooth pulled') uses ~てもらう ('receive the favor of X-ing') to frame the dental work as a service performed by the dentist for the patient. Japanese leans heavily on ~てもらう for procedures where someone else acts on the speaker's behalf — even something unpleasant like a tooth extraction is grammatically a 'favor' received. Without this auxiliary, 歯を抜いた would be ambiguous (did she pull her own tooth? did the dentist?), and 抜かれた (passive) would frame it as something done to her against her will. The てもらう strikes the right balance: she had it done, by request.