Try a little toothpaste on an old cotton T-shirt, rub until dry, then polish residue off with a clean section of cloth. Meguires also has a plastic polishing compound that would work fine. I have it around for polishing minor scratches out of CDs and DVDs; some of the ones I borrow from the local library aren't in the best of shape.

PS I wouldn't want vinyl in long term contact with paint either, so I don't see how Topeak dinged you over. Clear silicone tubing would be a better choice. It also looks like you could also just wrap it with a strip of old T-shirt or some wool felt and be done with it. Of course, if those get damp/wet, and lay against the paint for some time, you get marks too.

BTW, you, the consumer, decided it was an appropriate product for long term storage. I see nothing in Topeak's description suggesting that is what this device is intended for.