The owner of the Domino's franchise in Conover, North Carolina, has also filed a criminal complaint against Michael and Kristy, as the workers are known on YouTube.
The videos, which were filmed by Kristy, feature Michael putting cheese up his nose and rubbing a cleaning sponge between his buttocks.
Warrants have gone out for the arrest of the pair, who were also sacked by the owner of the franchise.
Kristy has told Domino's that the videos were a prank and the food was not served, but a Domino's spokeswoman said the company was "not in a forgive and forget mood".
Following our earlier story on the videos more details have emerged of how Domino's came to learn about their existence.
They were spotted on YouTube by staff at Consumerist.com, a blog run by Consumer Media, the publisher of Consumer Reports.
They called the store as well as alerting Domino's corporate headquarters.