I'd tell her that, once a relationship gets to the point where you're calling him your ex and still want to check on him, something's wrong. She should take a close look at herself. Jealousy is often the product of insecurity. She needs to deal with that, not her ex. I would also suggest this would make a good math project for her. She should learn how to calculate odds and look at the chance of guessing a password. She might be an old lady before she gets an answer that way.
Bottom line, I'd be more concerned about why she feels the need to do that than the fact that she tried.
overall should she be at the least concerned about like getting caught, etc.
As long as she only tried to guess the password, I don't think so. If she tried to hack the system someway, it's a possibility if there was a complaining victim but how would they prove that if she was unsuccessful? Most of the Internet policing is directed at money issues, not boyfriends. Tell her to be quiet about what she did and learn from it.