A cat with nothing to do and a cat with too much to do should look different. Like a confused sprite. Maybe the confused cat will even look back and forth between its options.
Controls are annoying:
When I see a cat moves into an adjacent square, I click somewhere else, but it doesn't do anything. Then I realize I have to wait for the moving cat to slowly go the last few pixels. Then I can make another click.
For a puzzle game like this, the time it takes to solve a puzzle should be limited by the player's ability to think and click, not how long animations take.
An easy fix: If an animation is running, clicking to place another house will instantly finish all the running animations and then place the house.
Make Z and R do undo/restart
Make undo history carry across restart, so I can undo a restart.