I'd try a little mineral spirits on a rag and if that didn't do it maybe some acetone in an inconspicuous area first.

Do you think that is just dirt? I was thinking the glaze came off perhaps.

Sure looks like the topcoat and glaze has been worn through based on the picture....are all the doors doing this around the knobs/handles?

"Do you think that is just dirt?"

tfitz1006:

Yes, but I was trying not to say so. I'm working on my tact.

Ha ha it is not dirt, I'm a pretty good housekeeper. I think that the topcoat and glaze are worn off. It is the same on most of the cabinets which receive daily usage.

Have you considered using a backplate to cover the worn area rather than try to touch up the finish? I have backplates behind all cabinet knobs in my new kitchen to avoid the same wear problem that was experienced in my last kitchen.

Acetone or mineral spirits will remove down to the wood. I like the idea Texas Gal has using a back plate. Or even new knobs with a wider base. Painting, antiquing and sealing would be a tough call to match.

Here is a link that might be useful: Back plates