Most of the time, adhesive hooks will come off clean without damage to the surface it was stuck to, or the hook itself. However, if you're having trouble removing bits of a broken plastic hook, try this method by Sarah, aka Thrifty Decor Chick:
"Cut off a decent length of dental floss [from Amazon] so you can grip it well on both ends.  Moving it back and forth, wedge the floss behind the plastic part — if you can get it behind the sticky stuff, that's great!" she says
"Wiggle it down behind until it reaches the bottom. Your hook will come right off! If you have fishing line [also available from Amazon] that also works great for removing stuck Command strips!" she adds.