This all depends on how deep the scratches are. Stainless steel is really tough metal but scratches easier then carbon steel.
If the scratches are deep, you can use very fine wet or dry sand cloth with a large rubber eraser as a sanding block.
You have to do this with care so you don't dish out the area.
If scratches are too deep either leave it alone, or send it to a top professional gun refinisher to have it professionally re-done.
To remove finer scratches use the Scotchbrite pads that can be bought from automotive supply houses. These are sold for auto painting.
Some hardware stores sell them in smaller sizes in "grits" equivalent to steel wool.
You can even lightly use the green pads sold in grocery stores.
Polish out the scratches, then finish by "stroking" the pad in one direction, matching the direction of the original grained finish.
If you just rub the area, where you reverse the pad will leave circular scratches, so stroking in one direction prevents that.
You can use a metal polish like Flitz, Mother's Mag, or most any quality metal polish.
This will leave the area with a too shiny finish so finish with a Scotchbrite pad to restore the satin finish and even it all up so you don't have a varying look.
Another trick to even out the surface and dull it slightly requires totally disassembling the gun.
With the gun totally disassembled, mix up a cleansing powder like Barkeeper's Friend with water to form a paste.
Use a brass toothbrush and the paste to "scrub" the surface to blend and flatten the finish.
NEVER use steel wool on stainless ore aluminum.
Tiny particles of the low carbon steel will embed in the metal and can rust later, ruining the surface.