Speaking to NBC on Wednesday, Ms Ness said she and her son had been informed of the crash by ground staff at the airport in Melbourne.
“They said: ‘Look, we’ve traced your cat – but it’s actually on the flight back to Christchurch…’
“And I said: ‘When did you find out the cat wasn’t taken off the plane?’ And they said: ‘We have just discovered.’ And I said: ‘How can this be?’
Ms Ness said she had been told the pilot had already been alerted to turn on the heating in the cargo hall where temperatures could drop to 7C.
The incident is still under investigation, but reports suggest a stowed wheelchair may have obscured the baggage handler’s view of the mitten cage.
Air New Zealand has apologized for the inconvenience, promising to reimburse all travel expenses.
The company does not accept direct bookings of animals from the public for international flights, so passengers should book through approved pet carrier firms.
Ms Ness said she was relieved to finally be reunited with Mutton.
“She basically just ran into my arms and crawled in and just had the biggest purr ever,” she was quoted as saying by the AP news agency on Wednesday. “It was just such a relief.”
Ms Ness, who had previously decided to move to Australia, added: “It wasn’t a good start to our new life in Melbourne because we didn’t have a family, we weren’t complete.”
A one-way flight between Christchurch and Melbourne usually takes less than four hours.