Child behavior..?

Recently a neighbor child has been playing with my daughter and I was happy as my kid got somebody to play. At first she used to spy around house and visit at us during my daughters school hours (online) and disturb the classes. It’s like this child doesn’t want to follow any rules or respect others privacy. The parents appear to be good but hardly available to talk and totally ignorant of this child. The child behaves more like a spy, inquiring about our plans, my daughter’s status in classes and sometimes says in a creepy voice that she is following what my daughter is learning etc. it felt more like an adult talking out of a child mouth. Even if I put the chain on the door, she would force herself inside asking why she can’t be inside. She even joined same extracurricular acitivities as my kid and seems to follow strictly what we are doing and competing with our kid rather than enjoying playtime. I am worried for this kid future as well as my kid and don’t want to my kid to learn this horse race attitude. Recently the kid joined my kids same extracurricular classes and follows her status and talks demotivating to my kid. we bump into that child somehow and my kid seems upset because of this.  

I talk to my kid to ignore things and concentrate & enjoy rather than getting disturbed. It feels like that kid is invisible following us always.  It’s mostly in other classes that we bump into each other. Wonder how to fix this without causing troubles with the kids parents.