DON'T USE STEEL WOOL.
Tiny particles of the steel wool will embed into the stainless and can rust, ruining the finish.
The correct product to use are Scotchbrite polishing pads. These are similar to the green synthetic pot scrubber pads sold in grocery stores.
The best place to get them is at a good automotive supply house where these are sold for use in painting cars.
They come in various grits, so buy several grades so you cna match the original finish on the gun.
To use, rub until the scratch or marr is either gone, or if deep, until it's blended in. Finish by stoking the pad in the same direction the original grain ran.
By stroking the pad you avoid leaving tiny circular scratches where the pad reversed direction.