If you can somehow "subtract" the code of the JOKER FIGURINE from the code of the poster, it might work.
Luckily, the Joker code only has two holes, making the task very simple. The defaced Cosby poster shares those holes. You determine that the defaced Cosby could only result from a double-punching with the Joker, if your theory is correct. This means the original Cosby poster had one of those holes punched, or the other, or neither, making three total possibilities.
You try out all three possible codes, yielding:
- 1 POTTED PLANT
- 1 PAINTING OF A HORSE ATTACKING A FOOTBALL PLAYER
- 1 CLEAN COSBY POSTER