Refinish the whole top of the table to fix it and always try putting an old pillow under our feet when we rest them on the table.

It's possible that the oils from the feet have eaten through the finish, but it may just be a reaction with the cleaners/oils that have been applied. First try cleaning off all the old polish and applying a good paste wax. If that doesn't help, you may well have to do a refinish job. Regular spray polish doesn't protect the wood finish as well as a good paste wax.

An option after you fix the spots is to have a glass top made for the table if it is a valuable piece and you can't get people to stop putting their feet up on the table. You could also consider replacing the coffee table with an ottoman.

Here is a link that might be useful: Wax/Polish/Oil Article

What I have found that works for white rings left on wood surfaces from people not using a coaster, is spraying a bit of WD-40 on a rag and rubbing the area. I've done it on a oak wood veneer table and just fixed a spot on the oak TV stand. I didn't have any WD-40 handy, but used Liquid Wrench Super Lubricant and it worked just fine too.

You might try using one of those on an inconspicuous spot before trying them on the top. If you try it, please let me know how it works for you.

Sue