Granting screen recording, and why it is required

This sounds like a permission you can decline and keep the product. It is in fact the precondition for the whole claim: macOS will not let a window exclude itself from a capture it cannot see.

It is also how the app reads what is on your screen — the region screenshot you send along with a question.

System Settings › Privacy & Security › Screen & System Audio Recording, tick MoPilot, then quit the app fully and open it again. The setup screen notices on its own once the tick is there.