How can I remove these stainless steel scratches?
I can't tell from the picture, but ideally, if you can remove that piece and work on it freely, here's what you can do:


Use a scotch brite pad and uniformly create scratches (the trick is to always always go in the same direction). This pad here is commonly used to mimic #4 finish in stainless steel. You can also go to heavier / coarser pads.





If you actually have gouges, and assuming you have access to an orbital sander, like this one (example), you would use a heavier grit pad to blend in all the scratches, then gradually go to a finer grit, 600 / 800 or so, to make all the scratches disappear. Then you can, if you want, put a grain on it again with the scotch brite pad.





To finish it up, you can clean the stainless steel with stainless steel cleaner and polish.