How to properly clean gunky CDs?

Years ago Cd's in box sets used to be packed with foam inserts holding Cd's in place. I probably should have removed the inserts at that time because now I find that some of them have deteriorated to the point where they leave a sticky substance and bits of foam on the non-playing side of the CD.

I have tried plain soap and water, alcohol, and even lighter fluid. Nothing removes this gunk and I don't want to insert the CD in my player and risk gumming up the mechanism. Any recommendations as to how to remove this gunk would be appreciated?