Q: Does the Mouse Mask recharge after Luke Robinson triggers the Gate Box which puts into play Dream-Gate: Wondrous Journey? How about when the signature weakness Detached from Reality puts the other Dream-Gate: Pointless Reality into play?
A: Yes to both; in both cases, Dream-Gate is “put into play,” replenishing an offering on Mouse Mask.
Note: Not sure how to add this to the FAQs section above, but this is the official answer I got from FFG.