Michizure says 'when'. Michizure says 'if'.
This is how the IRL game works, but to simplify- Michizure is a little more picky on the last thing happening being the destruction. GHQ mills after the card is destroyed, though the wording is before the Problem Solving Card Text update.
Basically, warm worm doesn't care because it says If, but because Michizure says 'when', you can't use it here.
Warm worm destroyed by battle (mil 3), revived by regretful rebirth, at turn's end got destroyed by rebirth's effect (mill 3), which makes it revivable by Puzzle reborn, then assault on ghq (mill 5). That's one of the ideal combo