You don't need a key. If you have Orca jump and Double jump (which if you've already backtracked to Deep Town you will probably have) then you can locate the nearest platform (right pathway of house) and blast over, jump twice (once with double jump, twice with Orca jump) and access the house.

Be warned, this requires a TON of trial and error.

The door for plot development is below the house (you can see it when you are outside)