Don’t really know for sure, you may want to ask Bib. Best guess I can give is that it is some vinyl type product…or maybe a silicone/rubber gel. Reminds me alot of the same type of product (various plastisols) that are used to make soft plastic lures. That’s what puts my mind to vinyl plastisol, the reaction to other forms of plastic is similar. The stuff in the BH, if it is a plastisol type substance has either alot of hardener and not much, if any softener.
Be warned, if you set the BH down on a plastic boom box with the gel touching the plastic, it may indeed leave an impression over time. Whatever amount of softener is in the gel lining is enough to soften other plastics by leaching out. Get a nice Plano “wormproof” tackle box for long term storage. Just kidding there, but the gel can damage some plastics if left in contact.
If you are replacing, best to contact Bib. If you’re looking to modify, try some plastic/plastisol companies for info on types of plastics. M-F Plastics or Calhoun are some of the better manufacturers, but rather pricey. Not even sure if that’s what it is, but they do make many grades of plastisol, so it’s a start for you.