Mimi- I may have found our answer (thanks Google).

OXICLEAN! This stuff does the trick. I use the powdered formula, mix with some warm water. Use an abrasive kitchen sponge - the kind that are "scrubby" on one side. Gently scrub the tape with the cleanser and let it sit on for a few minutes.Wipe off with the non scrubby side of the sponge. Scrub harder if your tape is particularly dirty.
Anyone else have any suggestions?