Remove the pulls/knobs and reclean with TSP---or whatever is sold as the replacement. Then lightly sand the sirfaces and try touching up the scratches with touchup sticks---rubbing in the compound with your finger.

Then recoat with varnish.

Sherwin Williams has a good regular varnish---and the TSP stuff. Other paint stores---NOT home improvement stores---real paint stores will have decent varnishes as well.

I used Restorz-it on the kitchen cabinets in our old house, prior to selling it. I only lived with it for about a year, so I don't know about its long-term durability, but it did a decent job. It did come out shinier than the original finish. Still, they weren't particularly high quality cabinets, and they were very detailed, and Restorz-it was a quick fix. WAY easier than stripping, sanding, etc. I know purists won't agree with me, but it's a cheap and easy temporary fix. Easy enough to touch up when needed also. Good luck.