Greenies chew removed hard piece of tartar?

I gave my dog a greenies chew the other day and a day later, I found a flat piece of what seems to be hardened tartar next to his chew toy. I found the tooth that it seems to be chipped off of, and the tooth looks undamaged underneath. I didn’t think the greenies would remove hardened tartar. Has this happened to anyone else? (I know I need to take better care of his teeth, and I discussed doing a cleaning with my vet) Would this been something to get checked out by a vet?