Today’s Mother Goose and Grimm, with two seals:
The cartoon turns on the ambiguity of seal — the device or design, or the animal. Then it depends on the existence of the Good Housekeeping Seal of Approval:
So it also turns on the ambiguity between the proper name Good Housekeeping (name of the magazine) and the phrase good housekeeping ‘keeping house well’ (with a common noun head). But in the cartoon, the seal on the left is a no-good housekeeper. (I’m guessing that Mike Peters, the cartoonist, intended the seal on the left to be male and the one on the right to be female. Gender roles appear in surprising places.)
The pun has something of the flavor of a phrasal overap portmanteau, but can’t be exactly analyzed that way: it’s essentially no-good housekeeper + Good Housekeeping Seal (of Approval).