Evade responsibility. Not have to complete a requisite chore. Receive a lesser penalty or no penalty at all. ‘Hook’ refers to guilt so get off it is to elude conviction.  (Compare to Wiggle out, Duck out, Weasel out, Wormed out or Cop out.)

“The teacher wanted me to stay after class and help re-arrange the chairs, but I told him I had to go ball practice, so I got off the hook.”