Depends how deep the scratches are. If they're significant, there's nothing to be done; if they are minor you could try buffing them out by hand with extremely fine steel wool (Grade 0000). However, be aware that, depending on the surface finish of the stainless, the area you buff may end up with a slightly different appearance, and then you may feel the need to go over the whole surface to get a uniform look, which could take a very long time and a lot of elbow grease.

I've got some small scratches on my stainless cooktop, and I decided that I'd drive myself crazy if I tried to buff out a minor scratch every time one happened. Sometimes the fix is worse than the problem. You may want to think about the old saying: "Don't fix it if it ain't broke."

Do not use carbon steel steel wool it may result in surface rust on your stainless steel. Try 220 sandpaper and scotch brite pads.

By all means pay heed to mrclancy's advice. Any time stainless steel is traumatized by carbon steel, there are iron molecules transferred into the surface of the stainless, and they will rust. There is brass "steel wool" but brass isn't hard enough to make any change int he stainless steel surface.

If you use a light touch, you can improve surface blemishes in stainless steel using an angle grinder with a stainless steel cup brush. Also, if you have an angle grinder, welding supply houses can fix you up with surface conditioning pads with hook and loop attachments to a circular pad which goes on the grinder shaft. Walter makes a kit which has a pad holder, tow or three different textures of pads, and a felt burnishing pad.

As kudzu mentioned, you won't be able to bring your repair to exactly match the undamaged area, so you might be in for a project which will involve going over the entire cook top to make it all match.

I you use sand paper or Steel wool you run the risk of leaving a bright spot.

You can try a restoration DIY kit called Scratch-b-gone. It has been very sucessful in removing scratches from stainless steel. I recommend calling the manufacture and they should recomment it to you

Use scoth-brite pads.

Depending on the surface (high polish or brushed) you start off with a relatively coarse pad to remove the scratch, then use finer grits to match the surface.

A bright spot in a brushed surface is easily blended by using a coarser grit.