if you are using synthetic tape, it'll clean up a little better than if you are using cork tape, but pretty much once cork tape has taken on the grungy look, it either looks really grungy, or slightly less grungy. You can use some warm water and a drop or two of dish soap and some light scrubbing action, take it easy on the side to side scrubbing. Use a sponge or an old terry cloth towel, once you are feeling statisfied, or fear you are about to mess up the tape it's time to rinse the soapy scum water off with some clear water and you should see a difference. Keeping any light color bar tape looking pristine is pretty much a fantasy... that's why my yellow bar tape looks the way it does.
HR