Coarsepaw ate it. That part where he was completely silent why they discussed why they were going to help Coarsepaw be leader instead of Brokenfang. It wasn't extremely important...just a symbol. I put it in the thunderpath scene to make it cooler than him just ducking under the car...and when Midnightnose didn't allow him to put it on the fresh-kill pile, and all that other stuff when we learned he had tossed it infront of Coarsepaw on the thunderpath, when they all were kind of playing with it was to show the lack of care that group of cats has for prey and the Clan. You know how warrior cats are to be thankful of the lives of prey they take so they can live? I think it's been mentioned everyone in a while...and once in the books atleast. They have no care or appreciation for it.
And it should slowly make more sense as the first part ends...which may not be for a while, actually. Though motives may be unclear, the actions they take will eventually be wrapped up by a purpose. I'll just put it out there that chapters throughout this section will have either timeskips or just be at the meetings of the cats, like in the last chapter, where important conversations take place. Coarsepaw may not take notice to them...but they'll be pretty important.
Lastly, I'll end my rambling by saying if you don't understand something, go ahead and ask. I may be able to make it less of a puzzle.