I think this is similar to a third conditional, if not exactly that, if by this phrase you mean what is described here: https://www.perfect-english-grammar.com/third-conditional.html :
It talks about the past. It's used to describe a situation that didn't happen, and to imagine the result of this situation.
If she had studied, she would have passed the exam (but, really we know she didn't study and so she didn't pass)
That is almost what's going on here, though this is a (rhetorical) question and there is no "if" clause. Callie is making the point that she had no opportunity to get a toothbrush. She asks how it would have been possible for her to get a toothbrush, but not actually expecting an answer, since this is a rhetorical question, and the answer is clearly something like "There's no way I could've gotten a toothbrush."
A similar effect would have been achieved if Callie had said the following*:
If I hadn't just come from juvie, I would have gotten a toothbrush before coming here.
*(note my use of the third conditional here!)