I would not tell her. You are thinking of her and you do that times other than when she may be having a difficult time but you do not tell her then do you, every time you think of her? I would discuss the whole thing with her in your next session, "I was thinking about you when I read about the school problem and thought you would be having a busy week and wanted to tell you. . ." If you think it through, it could be a bit intrusive; you don't know what her week is going to be like, you are imagining it. You are not part of her life and you are trying to be part of it without being invited? You have invited her into your life through therapy but she has not invited you into her life. That is what understanding boundaries is about.