That doesn't mean they'll replace it if you simply didn't like your pizza but they will replace it if your pizza wasn't made up to their standard with problems including "temperature (cold), undercooked/overcooked pizza, skimpy toppings, wrong pizza/toppings, and damaged pizza."
You can find the details as to how to claim the guarantee on the Papa John's website here (in case you're wondering, if you've eaten more than two slices of the pizza, they won't replace it).
According to the fine print, the guarantee only applies to the quality of their pizza but not their sides, drinks, or desserts.
To promote the new guarantee, Papa John's is offering an online deal for a large with up to five toppings for $9.99 through March 13, 2016.
Photo via Papa John's.