Worst than the lingering, you approached the same THREE times in same day. If you had lingered, built up your courage, did a bad approach and left it, she prob wont have reported it. Look at it from the chick's point of view. If you've interrupted her 3 times in the first day, you're prob the guy who is going to talk to her again the next day and the next and the next.

Also, you're not joining that gym because they told you someone reported you? Guess what, any business where customers are reporting you, they're going to tell you. No gym is going to have women tell them they're uncomfortable because of this guy and the gym is just going to say "whatever." Especially for an already paying member while you're new and havent even signed papers. If you did this in a restaurant, ie go up to someone having dinner 3 times to have a conversation, dont be surprised when the manager has a word with you.

Next time dont linger, and please keep it at one approach in these environments if you're opening cold. In environments like the gym, do warm approaches, or the occasional cold one and move on.