A screen to keep wasps from building nests in a gun barrel might be a good idea, but I don't think that's what these mystery items are. But I have no clue and haven't even submitted a wild ass guess.
I did once come very close to pulling the trigger on a 20 ga. shotgun that I leave in my garage when something told me to stop and check the bore. It was packed solid with a mud dauber wasp nest, and certainly would have blown up. The little bastards will nest in any small opening, and once did the same thing to the bore of a .177 cal. spring piston pellet rifle. I now cover the muzzle of my garage gun with an oiled rag to keep critters out.