On the comment on her just showing up now it may be because the year long banishment just ended. Before now, Kuzuhana could have still been banned and the new girl didn't care. Now that Kuzuhana has given the reason for not returning to the gym then its a legitimate concern to bring up to her friends. New girl also probably didn't mention this earlier because she had no reason to. She isn't pushing them away for safety, she wants to isolate Kuzuhana so she returns to the gym.
Also, pretty much every girl in this school has had ulterior motives when we meet them, so this is not surprising that the new girl acts this way.