when I had parts done for me in stainless for my motorcycles or even on the boat usually I just let it be...however on pipes and headers I polished them up with a metal polishing paste
usually that does it...however its not really a bother, more important is if the welds were done well and the stainless was the same type...cracking and low penetration happens a lot when a new piece is added to old hardware...
Typically the process after welding is flat grinding, flat sanding with successive finer and finer grits, then polishing with 'white metal' buffing compounds (clays containing diatomaceous earth - "Tripoli") to a mirror finish using high speed fabric buffing wheels, .... then if better corrosion resistance is desired electropolishing.
Don't be tempted to miss out a single grit step though, you'll be sorry.
I recently wet sanded an entire car, with 400, 600, 800, 1000, 1200, 1500, 2000 grit , then machine buffed with the Turtle Wax buffing compound, then with polish, then wax. Well, it looks good now. Wasn't much fun at the time.