This is a direct reference to excuses allegedly used by the notorious tourists to avoid paying for meals when eating at restaurants.
However, the pizza does come with an important and highly specific condition:
"Terms and conditions: Only available to notorious families of rabble rousers who have stolen a rope, trashed a beach, and received a deportation notice in the last seven days. @John Johnson, drop in to any branch of Hell in New Zealand to redeem your prize."
A spokesperson from Hell said that if the infamous troublemaker did turn up, the team at Hell would gladly whip something up for him. What that something might contain was, however, not revealed.
The spokesperson added that Hell simply couldn't help but become part of this conversation.
"The last seven days has seen the most egregious violation of New Zealand sovereignty in living memory, as a roving band of ne'er-do-wells has instigated a string of outrageous incidents across this fair nation," the spokesperson said.
"They trashed a beach, threatened people with violence, engaged in petty theft, even dined and dashed from respectable restaurants (and a Burger King).
"Hell Pizza, not content to sit on the sidelines, has decided to join the conversation."
The ad campaign was developed by agency Barnes, Catmur & Friends Dentsu, which has long pushed the boundaries with its advertising work for the Kiwi pizza company.
Barnes, Catmur previously provoked controversy in 2014, when it promoted its limited edition rabbit pizza by pinning actual rabbit skins to a billboard.
Air New Zealand has also (more subtly) referenced the travellers in its latest Grabaseat campaign, showing a singlet-clad man escaping from a littered beach.