My neighbor gave me this orchid because her cat was chewing on it. She was afraid it would die. I potted it in new medium so I could look at the roots, they looked pretty good. What should I do about the damaged leaf? Can I cut the black parts off? Or should I just leave it alone?

You can cut the black parts off but only for aesthetic reasons as the plant really doesn't care.

Is the photo before or after the repot

The photo was before I repotted it.

Lucy 68 is correct, The plant really does not care so long as you cut back just into green healthy tissue. Be sure to use a sharp blade that is clean and sterile, and make a clean cut all the way across the leaf. The plant does care if you give it a virus or some other disease from another plant that you have cut. Bill

Physan 20 is a good disinfectant to use to sterilize tools