Gas cap "anchor"

Went to fill up the tank and the little rubber "anchor" on the end of the gas cap retaining cord popped out of its metal hole. It didn't feel very flexible anymore. Today was very hot, and maybe it was one very hot day too many. Pushed the little rubber plug back into the hole but its grip has gone.

It looks like that bit of rubber and its tether is not separate from OEM gas cap 77300-47010. Or is there some way to replace it? A new cap would be around $25 which isn't much but seems a little ridiculous in this case since the cap works fine otherwise.

This is the only car I have ever owned that had a tethered cap like that, and since the car still has a place to rest the cap on the little door while fueling, I'm thinking maybe just cut off the tether so it will be like all those other cars. Don't want to leave it flapping around loose. With my luck that loose tether will somehow manage to eject the little rubber plug into the filler tube at just the wrong time and somehow break the fuel pump.

 

Put that material in the hole and put the no longer grippy piece into that (glue it in)?

Or put the not grippy piece in the metal hole clean and cement it in place with a blob of one of those two materials?