Wright and Jeffrey said their parents were concerned the young couple were rushing into marriage.
The couple decided it didn't feel right so did not show up at the booked time.
"We didn't want what's meant to be our happiest day to end up being a drama so we decided not to go through with it. Nothing has changed though. We still want to get married and spend the rest of our lives together. I love him more today than I did yesterday," she said.
The couple said they would set another date, and let all their friends and family know.
"I don't want a big wedding though. A big white dress is not for me," Jeffrey said. "We just want it to be a happy day for us and to have nice food and share it with our friends. We have been through a lot and it's been worth it to me," she said.
"People just assumed we were getting married so I could stay in the country but that had nothing to do with it. We weren't even thinking about residency," she said.
Jeffrey is in New Zealand on a permit to work at the West Wave Aquatics Centre swim club.
She is due to renew her work permit and one day wants to coach West Auckland Aquatics.
She returned to the US for two months to try out for the Olympic team but missed out.
"There were a lot of people there that I had looked up to as a kid making comebacks so just to be part of that with them was amazing. I do want to try again in four years' time. I'm still only 25," she said.
Wright has left school and is now working at West Wave Aquatic Centre as a lifeguard but wants to join the police.
He tried out for the Olympics and missed selection but is ranked among the top 10 male swimmers in New Zealand.
