We don't have any issues with you adding copy protection. The way to do it would be to verify with the itch.io API that the person running the game actually owns your game. You can use our server-side API to accomplish that: https://itch.io/docs/api/serverside
Games launched through the app are automatically passed a JWT API key. If you'd like to have the same protection without using the app then you'll need to implement "Log in with itch.io" using OAuth apps: https://itch.io/docs/api/oauth