I should have provided more detail about that ring of metal.
So, the bike was on its side stand. I think the low fuel caused more sloshing when I pushed the bike upright, providing less cushion to the ring when it moved. I usually use the center stand, so that may be why I never heard it before when moving the bike. (There's enough room front to back that the ring wouldn't hit the sidewalls of the tank when getting the bike on and off the center stand, but lateral motion made it strike the side of the tank.)
When I moved the bike upright, I heard metal clanking in the tank. I moved the bike sideways a few more times to make sure it was coming from the tank, and it was clear it was. I popped the cap and peered in with a flashlight. The ring was sitting in the right front lobe of the tank. It looked odd, but I assumed it could be a baffle or maybe some protective piece for some sensor and at first ignored it. I didn't see anything else in any other part of the tank (though the view inside from the filler is obviously limited), so I wiggled the bike while looking to see what moved. The ring immediately slid back, so I knew it was unattached. I got a magnet pen which grabbed the ring easily. It's completely free floating. In the picture, I pulled it up to the filler hole to make it as visible as possible.
It's a much wider diameter than the filler hole. I don't know if the fuel pump hole is large enough to get it out either.
But even assuming I can get it out, that still leaves the question of why it was in there in the first place. Was it supposed to be under the filler hole to protect from fuel spray or something? (This is the only Enfield I have, so I don't know what the inside of another tank looks like.) Is it supposed to protect the fuel pump? It's a solid circle, with no holes, indentations, or cutouts on it. If it has a function, removing it isn't really the solution—having it put back where it belongs is.