We recently had our hardwood floor redone and 3 months later put a good area rug on top. The foam padding has a grid of small holes and now we see the pattern of the padding in the wood stain! I need to get rid of this before we sell the house. Any suggestions?

Saw that problem once years ago when I first started doing floors. The guy I worked for screened and recoated the floor and it was still there. I know that my info is of no help, but I hope someone will answer with a good reason/remedy.

Those square holed foam area carpet pads are anathema to wood floor finishes. They should be illegal. I always caution my customers to not use foam pads under rugs. Either do not use pads Or if the rug slides to easily, a little double sided tape here and there. Note the term a LITTLE. Not much can be done. It may fade gradually.

Well you haven't been given any great ideas so far, and unfortunately I am not going to be too much help either.
Two things: offer the purchaser a credit equivalent to the cost of refinishing that room, or alternately, ask them if they like that carpet.
I know that wasn't much help but its all I got.

Does this happen because of the oil-based rubber?

Well, it is definitely a chemical reaction between the finish on the floor, and the composition of the underpad.

I've had that stuff stick to my waxed floor as well. I switched to a thin synthetic carpet fiber pad with no issues so far.