Forget oily solutions, there are 1001 people talking about using wd40 or other crap, this will only "fix" it at best, but overall, you'll end up with a disgusting, greasy rubber. This stuff deteriorates chemically, and needs to be completely removed. I've had a lot of experience with Thinkpads, and even newer lappies like the Asus G73jh. This was one of the biggest misfortunes invented in computing.
You need to use a solvent that doesn't attack plastic, just rubber. Isopropyl alcohol will remove, but needs millions of "rubs". I recommend using Ethanol because it is faster and less aggressive (use gloves). In my country, ethanol is a very common fuel for automobiles, and I usually buy it at the gas station, I don't know how it is in the United States, maybe you can find it in a chemical or agricultural product store. Gasoline and even diesel will also "dissolve" it but I would only recommend it as a last resort as they will attack the plastic underneath the rubber.