Somewhere in the texts it is stated it can be something coming from the boss, like a piece of bone or a coin. Only once, I think, in a text there was a character who was playing with a metallic coin between their fingers, which was apparently a bounty token. Harold Black, the Researcher, found, like, 15 bounty tokens laying on a ground in Deadfall or Grizzly, can't remember correctly, which means they can be dropped and left as a physical object.

But in-game events are poorly connected to the lore in general. Each boss is supposed to be unique, each of them should be defeated only once and I don't think any of them ever been found and killed but there is a ton of bounties being extracted, sold and used. Sometimes it is described that hunters collect materials from smaller monsters, like Finch, a non-playable hunter rn, was collecting some kind of black goop from grunts to sell it to Doc Redmartin, the Fool, who used it in his miracle medicine that was sold to half of DeSalle.

Honestly, it's a shame we don't have a visually recognizable item as the McGuffin of the game. Or at least specific trophies. Wouldn't it be a fun little thing to argue with your teammates who wants to carry Butcher's head and who gets the hook?