Can I move a movie rental from my Apple TV to my iPad? If I rent a movie on my Mac, I can move the rented movie to my iPad.

Can I do the same if I rent a movie directly on my AppleTV?
Quote from Apple Support Pages:
"Movies rented on your Apple TV are not transferable to any other device and can only be viewed on your Apple TV."

If you have a iMac or Macbook at home, rent it through that computer, and then stream it to Apple TV for watching there... Movies rented on that Apple computer can be transferred with a click over to your iPad.