Have the same on a late 70's Grand Sprint but also incorporates the brake lever boots with Motobecane 'M' logo. I believe the wrap was provided by Hutchinson. Rather like it but could see wrapping cloth over it. I certainly wouldn't remove it. As for the OP's and being slippery, perhaps it was at one time Armor-all or coated. Might need to just do a quick wipe with lacquer thinner.

When I acquired the Grand Sprint, a real barn find with major scuz and mold, thought the grips were a goner. The lacquer thinner cleaned them up to near new and now probably the best condition part of the bike....lol.

(Just after acquiring, a first quicky clean, air in the tires and test ride. Now stripped down for a mild transformation project for a grand-daughter and participate in C&V rides. Getting a faux team BIC look of the early 70's.)