Keep it up if it is in good condition otherwise it probably doesn't matter. It stays better looking that way. I would however cover it to protect from dust, dirt and damage when not driving. The towel would have been put in the fold of the plastic window as you are putting it in the storage area to protect it from scratches. You can buy a protective pillow from people like Corvette Central that I think work a little better than a towel in keeping the window safe from scratches. It is about three feet long and about 5 to 6 inches in diameter and it fits the full length of the rear window. Easy in and easy out without it slipping out of position when you close the lid. Good luck.