I don't think there is anything included with the factory warranty - only if you bought one of the warranties that include tires after the fact. I picked up a piece of metal, but it was in the tread, so I was able to get it fixed. Good Luck
Happened to me shortly after getting my 2012 DD...
I found out that if you take your new car to discount tire or other places like that, they can sell you a road hazard warranty as if you just bought the tires from them.
FWIW