I use one of these bristle brushes because I didn't know better, I've also even seen a few bristles fall out before & had me a bit concerned.
However I always end up microwaving for 30 seconds after, because by the time I've let the meat rest and turned off the grill my food isn't as warm as I want it.
So maybe I've been lucky, as I figure there would have been a reaction if there was metal in the microwave.
Anyways now I'm looking for an alternative, I'm thinking of using a large wooden spatula and let it conform to the grill overtime.