Dealing with mean kids

Hello trying to figure out how to get Paige to deal with the mean kids in her class without turning her into a brat herself. What happens is these kids know Paige is sensitive and find ways to pick at her until she cries or they know her feeling are hurt. This is the same little girl we've had problems with since 1st grade. Honestly I wish I could just let Paige kick her but that's not our way and Paige is not that kind of kid. This little girl will make it a point to say mean things to Paige one day and turn around and act like her best friend the next. She deliberately becomes her friend so she can find ways to hurt Paige! I can't file a complaint because it's nothing more than a little name calling or just saying things like "your drawing is stupid" but Paige gets so hurt by this girls remarks that it hurts me to see her sad and not wanting to go to school. I see so much of myself as a child in Paige, very sensitive and easy to cry if someone says something mean to me. Paige has friends, gets along with everyone, it's just this one little girl that pesters her. I'm tempted to have the teacher say something to her but I'm worried that will cause more problems. This little girl is being raised by her grandparents, they give her EVERYTHING and she is constantly making up stories and lies to make herself seem better than she is. I know she's unhappy, doesn't have any true friends and doesn't know how to be friends with anyone and that makes me sad. We've tried to have Paige tell her, you're not being nice and if you say stuff like that you'll never have friends, but it doesn't help. The girl is just ugly. I don't even want her in my Girl Scout troop and she's a kid that really needs scouts! UGH.

Sorry had to vent. I spent 20 minutes calming down Paige at school and made her stay. She doesn't want to because this girl will get other classmates that are easily lead to join in her teasing of Paige. And she's quick to do it when there are no adults within hearing distance.

Jodi