My dog loves playing tug but when I use a ball on a string she prefers to bite the string. Will this hurt her teeth and gums?

I don't usually play with a ball on a string until I've done a foundation with a tug first (which maybe you have done?) Anyway, there are training steps done with the tug that give me a way to communicate to my dog when they are right (where they grip on the toy, etc) and when they are wrong so I can make them out to start again. Once I have a clear communication system and great targeting on a tug then I introduce the ball on a string.

here's a short video that covers some things that may help, I've also linked some other resources below.
https://leerburg.com/flix/player.php/1547/Ball_on_a_String_Tips_with_Michael_Ellis

I prefer for my dogs to grip the ball, not the string or strap. I'm not sure whether it will be a problem down the road with wear on the teeth/gums but it certainly does affect the life of the string or strap on the ball and teaching good targeting technique on the ball saves accidental injury to your fingers or hands should the dog miss the ball.