On Android app it needs Claude GitHub connection with scope to act on my behalf! Otherwise it won't work in the app. Really do NOT like that!
Why does the remote control needs that? For what?
I rather use the common developer tools like termux or mosh etc. on a phone if I need that functionality.
You can scope it to repos. Make a repo just for what you want. That's your sandbox.
Make a throwaway GitHub account just for it and give it PR access to your private repos.
Same here on my iPhone. I didn't previously log it into my github account as I don't use github anymore, I use gitlab. So it wont find anything useful there. You actually only need to do this in order to be able to access the list of sessions. Even if you don't log into github, remote-control still works if you copy across the link that the cli tool outputs for you and just visit that on your phone. That's a bit of a pain though of course.