Use 3M Scotch Brite pads (the coarse grey one for sanding the scratch, and the fine maroon one for buffing and finishing). As long as you go WITH the grain of the metal it will work like a charm.

I say get "0000" steel wool, scrub with soap (in the direction of the grain, most likely horizontal), then use white polishing compound (auto parts store) and apply with a moist towel, also in horizontal motion. Several applications may be necessary. No damage has been done, you just have to get the grain back to normal.

so I guess this would work for my stainless steel sink too? yay!