Furniture and Furnishings - HELP! Foam pad stuck to dining table

I have a very nice cherry dining room table, well made, probably about 30-40 years old, dark cherry finish. She-who shall-remain-nameless bought a cheap table pad years ago, and put it on the table, under the tablecloth. We just removed the table pad today, for the first time in years. The foam stuck to the table top!

The table pad is one of those cheap things, thin white vinyl on top, bare green foam rubber on the bottom. It looks like the foam reacted with the finish on the table. The foam stuck to the table top. I have been able to pull the vinyl top layer off, and then I carefully scraped most of the green foam off the table using a soft plastic scraper.

Now, what I am left with, is the top of the table (wood) that is very dull, rough to the touch, and seems impossible to clean up. I've tried various mild solutions and nothing seems to clean or shine the table. It's like the finish is slightly crazed -- like maybe the foam reacted with the finish. It's slightly rough to the touch, and has no shine. I have even tried very fine steel wool (#0000 and #00) which helped a little, but still the surface is rough and dull.

Any suggestions before I get out the dual-action sander?? Or just throw in the towel and take it to a professional furniture refinisher? This is (was) a really nice, well-made table.

Mikaman

I would try some lemon oil or even Pledge (or other polish with oils). The oils may soften the residue enough to come off (along with some elbow grease).
If it's gotten in the finish, you'll probably need to have it refinished, in which case I'd take it to a pro.