To put up with someone or something means to endure them even though they are unpleasant or annoying, and this is what Amelia is doing.
Consider the statement "Amelia, I don't understand why you're enduring her inspite of the fact that she is unpleasant and annoying to deal with; surely you can find someone else who can do up your hair to your satisfaction. ". Is the statement "Amelia, I dont know why you put up with her; surely you can find someone else who can do up your hair to your satisfaction." false? Yes/no/unknown