It is literally the "tag" for the animal, in some places you just call and tell them that you killed an animal and describe it, however it appears in some locations, including the one the show was filmed require a physical tag to placed on the animal instead.
Hunting
Thanks. Didn't know that some locations require animals to be physically tagged.
I don't know much about the show or controversy. Considering conservation laws and such, I'm thinking the hunter would have to have a valid permit to hunt, and possibly have to obey local laws regarding tagging their harvest. No matter if someone's using firearms or primitive weapons, they've got to be within local laws or risk meeting the local conservation officers...
Whenever they show someone killing an animal (usually fishing or smaller snares) they display a text saying something along these lines: all hunting follows local and native jurisdiction. The controversy was due to the kill being a single arrow to the hind leg. Bleeding the animal for about 5h. Afterwards it was finally killed by rushing it at least twice with a knife. So not something I would call a clean kill.
Good point about having to register and tag the kill with the authorities. That would definitely explain the plastic on the carcass.
For the US, every state has their own rules, as well as individual sites on what you can do, how you can do it. If you're on a Federal site, usually it's a mix of state rules and Federal rules.
Part of the responsibility is to know those rules and follow them. Yea, it can get confusing and hard, but that's part of the deal, so gotta be done. Much better to pick up the phone and call or shoot an email and ask questions, than to not and get a visit...
In the US, conservation officers don't mess around. They definitely can be on the unpleasant end of FAFO.
This is the water, and this is the well. Drink full, and descend. The horse is the white of the eyes, and dark within.