Well, literally it's "comes from writ(ing)", but why it's written like that is about as arbitrary as why we have to say "I am going to write" to signify near time as opposed to *"I go to write" in English. It's just how you phrase recent past in French.
I guess you can think of it like "She comes from writing a letter"? There's no real way to translate it word for word, keep the meaning and make it sound natural though. Different languages just deliver meaning differently; best to think of it as simply "She just wrote a letter", in the same way that "going to write" in English doesn't signify actually moving somewhere else to write.