bounty hunter is almost correct, you need a bit WIDER and a bit heavier ( thicker) than a popsicle stick, so as to NOT dish any of the area you will be lightly polishing with some fine emery paper ( aluminum oxide? ) paper.....
make sure the side plate is on something like rubber so as to NOT slip around on you....can use "slave" screws or pins to hold things steady..........
and yes stay away from the markings, or as noted above , put some tape over them.........then blend in the polishing as you were doing.......those marks are from moisture under the edges of the grip panels.......and YES, the grips will hide them anyway.........sooooooooo

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dan
NRA Benefactor,PMA