On or off....? bearing in mind im 5ft 4inchs tall and that strap comes in a bit handy for me when i move the bike around.. (and hold the strap on jokes please)lol
Get rid mate! You'll soon get used to moving it about without...just keep a duster near by for the finger prints though
At the end of the day if its a case of you dropping it if its not there then keep it as its gonna look alot worse with cracks and scratches on it!