Hi William!
Welcome back to planDisney.
Yes! These were commonly known as "Bounceback Offers", and you're right - they were often found in Disney Resort hotel rooms, offering a discount on future reservations. They went away for a while, but now they can sometimes be found again in your hotel room (always subject to change).
Usually, a booklet will be left in your room for you ("Your Take-Alonng Guide to the Magic!") which is full of useful tips and information about the theme parks, water parks, Disney Springs, Enchanting Extras Collection, and services at your Disney Resort hotel (housekeeping, payment options, health care services, car rental, for example). Within this booklet, you might also find a card insert with details of returning bookings, similar to those that you are asking about.
These return booking offers cannot be guaranteed, but if you do receive one they generally offer a good percentage discount on rooms at all
Disney Resort hotels - Deluxe, Deluxe Villa, Moderate and Disney Value Resorts, for stays on select nights, providing you make your reservation within 7 days of your checkout date. If you don't find one of these in your room, stop by the Front Desk and ask if there is a current offer available - they may just have forgotten to leave you one!
Please come back and visit us if you have any further planning questions, and you can also
send me a direct question if you wish. We will be happy to help you plan your magical vacation at Walt Disney World Resort, and keep your eye on the
Disney Parks Blog for all the latest official news about events that may be happening during your stay.
Sue