I have seen of of posts similar to yours in the last day or two, and I'm assuming it's because school just started.
I will give you the same advice I gave everyone else. Use this as a life lesson on what a friend should & shouldn't be, and on how to treat people as you want to be treated.
Personally, I would not waste my energy trying to talk to the parent, because at the end of the day, you cannot control the other little girl, or how she is being parented. What you can control is how you parent your child.
This situation has been happening since our parents were in school, and before that, and it will most likely happen more than once. I'd rather my DD be a self confident child who chooses kind people as friends & loves herself enough to walk away when someone is mistreating her. I'd rather she knew how to deal with real life situations, and have coping skills for difficult situations. I don't want her putting all her eggs in one basket & feeling that she "needs" to be friends with a certain person. I wouldn't beg someone to be my friend, as an adult, and I sure as heck wouldn't want my DD begging to be friends with some girl who didn't want to be friend with her, anyway.