This door for

That's the one-way exit from Martleby Hare, a street in Groddle Heights*, which can be accessed from Rookthills Lays with a Green-White circle key. There's a similar one-way exit for Vicar's Peak located at Mossystep in Groddle Forest.

_{* The wiki is wrong in stating that both Martleby and Vicar's Peak are Seam Streets. They're actually part of Groddle Heights.}