Definitely take it out, your accuracy will go WAY up.
As for foam, just get some foam like what's in a sound studio, cushion, or gun case, and cut it into disks with 8-10mm holes in the middle. You can make some foam with holes twice or three times as big, and alternate those in a way where there's lots of little chambers, this will be quieter in some situations.
As for foam, just get some foam like what's in a sound studio, cushion, or gun case, and cut it into disks with 8-10mm holes in the middle. You can make some foam with holes twice or three times as big, and alternate those in a way where there's lots of little chambers, this will be quieter in some situations.