Here's a link that may be just what you need:
For fine scratches, cleaners such as Comet and Revere Stainless Steel and Copper Cleaner are non-abrasive cleansers that will gently buff stainless steel. They come in a dry powder that needs to be combined with water or as cream-based cleaners that go on the metal a bit smoother. Appliance manufacturers often make their own cleaners that are easy to find at home improvement stores.Sanding with wet sandpaper is recommended for deeper scratches. Sandpaper comes in various grits, so check first with your appliance manufacturer about which kind of sandpaper will work best for your stainless steel.If you have a lot of scratches, there are a few DIY scratch removal kits, such as Scratch-B-Gone or the Siege 63001 Stainless Steel Sink and Cookware Scratch Remover pack, that will take you step by step through the scratch removal process. These kits feature products similar to the two described above in one kit and will cost you a little more out of pocket. One piece of advice is universal -- always rub or buff the scratch with the grain of the metal. If you go against the grain of the steel, you'll only make the scratch worse!
Here is a helpful video... I need to do this myself! https://www.youtube.com/watch?v=o9b-MIsmTVs
I like to use Bar keepers friend: https://www.amazon.com/s?k=bar+keepers+friend+cleaner&gclid=EAIaIQobChMI3ZGQvojw5gIVCaGzCh3DfwWNEAAYAiAAEgLOI_D_BwE&hvadid=176943900147&hvdev=c&hvlocphy=9058203&hvnetw=g&hvpos=1t2&hvqmt=e&hvrand=8899503667002072517&hvtargid=kwd-6888310533&hydadcr=8683_9761181&tag=googhydr-20&ref=pd_sl_6od8hxbd0d_e
I also use a grate and the bottom of my sink to help prevent them for the beginning.
Vegetable oil rubbed in makes them less visible. Barkeeper's friends is supposed to work, I've never had issues but someone on here once said they made the scratches worse.
Hi Sarah, I used a scrub pad from scotch brite to test this and it actually works, hope it helps you, remember to rub with the grain.
Hi Sarah: This site should help: https://www.wikihow.life/Remove-a-Scratch-from-a-Stainless-Steel-Refrigerator-Door Remember, always go with the grain of the steel and not against it. Good luck
Thank you everyone for the helpful information