'01 Gary Fisher Tassajara; '03 Litespeed Blue Ridge; '04 Cannondale Road Tandem; '93 Schwinn Traveler
Yes, cut it off. I bought an '85 Schwinn Traveler for my wife that had that black foam on the bars. I just took a utility knife and cut it off, than re-wrapped the bars in cork tape. The bar under the foam was like new - very shiny, not like the exposed section, so there was no problem putting the cork tape on. It was the first tape job I ever did and it turned out pretty well. Figuring how to end the tape with those cap inserts took a little time to figure out.