Burger King staff also complained that the kids would yell obscenities into the drive-through speaker's box and were showing aggression and rudeness to other customers.
"When refused a refund/replacement food … the family would become aggressive … banging the counters in the arcade, as well as swearing at them."
Despite this, Burger King staff did not wish to pursue a formal complaint in regard to the behaviour, the OIA said.
"All [family members] were issued with trespass notices for all Burger King Restaurants throughout New Zealand."
There are 83 Burger Kings across the country.
There were four children, two of whom were infants, and four adults, present at the Burger King saga.
The family was served Deportation Liability Notices (DLN) later that day.
According to Immigration New Zealand, a DLN provided the family with the opportunity to give "good reason" why deportations should not proceed.
INZ did not respond to questionsabout whether the family provided a good reason to officials.
Tina Maria Cash, 26, who was part of the unruly group, the next day admitted theft charges in the Hamilton District Court.
The court heard that Cash stole a can of Red Bull from a Caltex service station at Albany on December 31.
On January 28, the family touched down in the UK.