While the exact origin of the phrase is uncertain, its use on the show helped solidify it in popular culture.
However, it's important to note that "See you later, alligator" was not exclusive to the "Howdy Doody Show". It was a common phrase used by many people at the time, and it likely originated from a combination of factors, including the popularity of alligators in American culture and the common use of animal-related farewells (e.g., "See you later, crocodile").