I hate to say this, but it's medically dangerous to take it out at this point. It needs to heal around the stud or else abscesses are quite likely to form in cartilage.
However, make her take care of it and, when it heals, (3 to 4 months is what I'd say; not truly healed, but the risk of infection/abscess is significantly reduced. Plus, at that point, it will still heal over quickly and not provide a permanent hole that she can just stick the earring back into.) make her take it out. It will be even more of a blow than just demanding immediate removal.
I am neither a piercer nor a doctor, but have been researching piercings for years and this is the advised course of action from the most prestigious piercers in North America.
Also, if she got it done by a piercing gun, Google "piercing gun damage" or something along those lines. Make her read the articles about infection, unhygienic practices, and side effects. Make her look at the pictures of damaged ears, noses, and nipples (can you believe that?!
: ). It might make her think twice next time.