I know it sounds morbid, but tossing the bird into the woods seems disrespectful for some reason. I could give it a proper burial, but that doesn't feel right either.
And so I thought I'd ask the internet if there's any way to honor its life through practical reuse...
My naive initial ideas: make jerky for my dog? educational skeleton display? throw it into compost?
1) Leave for something to scavenge overnight, eg a fox round here in London.
2) Compost heap.
There's enough bird flu doing the rounds that you want to handle it carefully and not feed it to pets, IMHO.