All you need is some fishing twine.... work from one end of the guard to the other using the twine as a saw to seperate the glue from the door. Once the ding guard is removed, take some rubbing alcohol or some other solvent that won't eat at your paint and scrub the residue that the glue left behind off of the door.... this is where patience and elbow grease come into play.
BTW, why are these things referred to as "door dings"? Aren't door dings (or dents rather) made from too many people opening their car doors into you in a parking lot? Just curious. Anyways, hope this helps.
-Jeremy