What to do about my girlfriend's ex-boyfriend? He wants to be with her.?

I was in the exact same situation, i had just gotten with my bf, and my ex still wanted to be with me, and I did exactly what your gf is doing, I didn't stop and really take action until my bf told me he was affecting our relationship and that it could not go on, because it was preventing us from being happy. Talk to your gf tell her how you feel.