Yes, Idaho requires that the hide and skull be taken to an IDFG office for tagging. Dumping the carcass will get you in a much deeper hole than admitting you screwed up.
Are grizzly bears an endangered species in Idaho?
They're endangered everywhere in the lower 48 where they're found. The feds MIGHT delist them in the near future but of course the anti's are fighting it. If they do, ID, MT, and WY will divy up the available tags and sell them for a very high price.