The Grinch's dog Max is never given a backstory in the original book, How the Grinch Stole Christmas, nor in the iconic 1966 Christmas special of the same name. He is simply the Grinch's pet and helpmate in the titular heist. Even the 2000 film adaptation starring Jim Carrey, which sports an extensive tragic backstory for the Grinch, does not explain where Max came from or how the Grinch adopted him. Like the Grinch's hatred for the Christmas season, "no one quite knows the reason" that this gruff loner has a dog companion. However, other media related to the Grinch has offered explanations.

A book called The Grinch Meets His Max came out in 1998, written by Antonia D. Bryan and based on an episode from the live-action The Wubbulous World of Dr. Seuss television series, which featured several classic Seuss characters in puppet form. The book provides an origin story for Max, explaining that he met the Grinch when the green-furred recluse had a terrible itch on his back that he could not reach by himself. Agitated, the Grinch tries to shoo Max away until Max proves able to scratch the Grinch's itch. Relieved from the itch and moved by the dog's compassion, the Grinch decides to let Max stay with him as his pet.