This helps you patch a door that has a cutout meant for a cat.

The thin piece is meant to act as a template against which you run a router bit with a bearing follower.  You size this to be bigger than your door's cat hole and then you temporarily attach this to your door.  Use the router to cleanly cut out the interior.

The “plug" shape can also be templated and cut out of stock using a router.  The stock should be the same thickness as the door.

The “plug” should exactly fit the shape created in the door using the first template.

The Openscad code, STL files and SVG files are all provided for your convenience.