Doors – How to remove this two-piece door hinge

Edit: Thanks for posting the photo, answer updated (see below).

Here is some general advice.

Since larger chunks of wood are missing, use wood filler to fill it in (found at any home improvement store). Use a putty knife to match the shape of the trim as closely as possible. After the filler cures, use sand paper to round it out.

You will also need to paint over the filler. Get a chip of the wood trim and take it with you to the home improvement store and get them to color-match the paint (you may also be able to pull a piece of the trim off the wall).

The other option would be to find similar trim at the store and replace the damaged piece. Some fancy trims can be tough to match, but what you have looks pretty basic.

For what it's worth, in the last place we rented, our rabbit used to gnaw on the door trim in our bedroom. We eventually trained the rabbit not to do that, but it took a while, and the damage got pretty bad. We repaired the trim using the above methods. We got our full security deposit back.

Short of reframing the door, I'd suggest taking a belt sander to the side of the door that sticks.