You don't actually have to get "paid" by check-out, but you have to make the request and start the process before you check-out.

From Marriott's Elite Benefits T&Cs: "If an Elite Member believes that compensation is due with respect to any aspect of the Elite Benefits Guarantee, he/she must request payment of the compensation while still a guest at the hotel, prior to checking out. Failure to request such payment prior to check out will result in a complete waiver of any right to receive such compensation."

This can be found at Marriott Rewards Terms & Conditions