Quick Answer: Yes grazing muzzles can certainly damage teeth. There are many different designs of grazing muzzle, some are soft, some are middling and some are just plain hard.
- A soft, strong one is the LiteBite Horse Muzzle does not damage teeth.
- A middling type is the basket type muzzles, often made of harsh material for strength
- Another soft one is Thinline, fine for teeth but does tend to break or they eat out of the sides.
- The there is a rigid touch plastic one, Greenguard. Very strong but does tend to rub and many complaints about tooth wear, bound to really.
Choosing the right grazing muzzle for your horse can be an expensive thing to do, buying several cheap ones that don't suit soon add up to the cost of a better one.
So you need to look at all the options and consider what is best for your horse. Nos. 1, 2 and 3 are expensive but 1 and 2 do last well, No. 3 less so.
The bucket muzzles are cheap and if they happen to suit your horse then maybe choose one of those.
Personally I would rather pay more and feel that I am getting the best possible solution for my precious horse.
https://www.horsemuzzle.com/blogs/grazing-muzzle-advice/which-horse-muzzle-is-best-for-your-horse