5Dropped by
the window closes permanently
Dungeon Guardians only patrol the dungeon while Skeletron is alive, and they exist to kill anyone who wanders in early. Beat Skeletron and they stop spawning, which means this pet is gone from that world for good. If you want it, you have to want it before you clear the dungeon.
killing something built to be unkillable
Its defense is high enough that most weapons register as chip damage per hit, so the answer is volume and distance rather than a big number. A long flat tunnel, something that fires continuously, and a lot of patience. Anything that lets it touch you ends the attempt instantly.
the pet has one quirk
The floating head spins occasionally, copying the boss it came from. It also refuses to teleport when it falls behind and just flies the whole distance instead. Toggling its visibility off and back on in the pet slot snaps it to you, or you can simply summon it again.
the name
It is shaped like an old bit key, the kind commonly and wrongly called a skeleton key. The pun does the rest.