How to remove scratching from stainless barrel?

[NorCal Mtn Flyer]

I have recently purchased a used Marlin 1895, .45/70 Guide Gun with a stainless steel barrel. It appears that the rifle was hanging in an unprotected rack in a vehicle and suffered some scratching on the top of the barrel.

What might be the best way to remove or minimize the scratches?

Picture attached (I hope).

[freonr22]

try simichrome http://www.competitionchemicals.com/ Some Napa auto parts have it, Orchard used to carry it, (call ahead of time)
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[kendog4570]

"Shoe-shine" it with a strip of emory cloth and maybe some light cutting oil. 320 or 400 would match the ground finish on your barrel. Try it underneath the wood to check before doing it on the exposed surface.

[M1A Rifleman]

It May not ever be perfect, but a scotch brite pad (Home Dept) may help. You will need to polish the entire barrel with the steel grain. The pads come in different coarse grades like sand paper. This is what is used to polish scratches out of stainless steel doors, etc.

[willssmithing]

Scotch Bright pads, not the ones at your supermarket. Find a good hardware store, they come in coarse, medium and fine, follow the direction of the factory polish on the barrel.