wouldn't put the sponge back in, looks like air filter.
The plastic insert in the fuel neck is commonly used in a usually unsuccessful attempt to stop fuel from a full tank sloshing out of the fuel filler under heavy braking, running off the front of the fuel tank, and all over the very hot exhaust headers and the rest of the front of the engine...... many of us have had that experience, usually more than once. I have spent all kinds of effort trying to get a stock fuel cap to actually seal, usually unsuccessfully. Best to try that fettling at time of painting the tank, you can adjust and bend tabs as necessary without destroying paint,
on my aftermarket carbon fiber fuel tank made by Boba I had him fit a flush mount and properly sealing aviation type fuel filler, with a separate pressure vent. The pressure vent has a drain hose that I run all the way to the back of the bike, don't want fuel on the hot exhaust or on the back tire.
the other interesting thing I have seen is where the usually leaky stock fuel cap actually seals and then there is a tank venting problem... is the fuel cap drilled through and a Dellortto main jet threaded in to provide a vent
the solution that was recommended to me is to never fill the tank more than about 3/4's, but sort of limits your range.