The Aussie Mates in the States program flies retired racing greyhounds to the United States and Canada, linking with 22 rehoming groups including in Seattle, San Francisco and Las Vegas.
Dallas Police Department also got involved, adopting a greyhound specifically trained as a PTSD companion animal.
About 500 dogs were rehomed in the program's first year, with operators aiming for 1000 to board planes in 2024.
But what's alleged to have happened immediately after two dogs arrived at Dallas airport in Texas in June has concerned animal welfare activists, despite those claims now being rejected by Greyhound Racing NSW.
After a 15-hour flight and with air temperatures reaching 32C, female dog Katana was found dead in her cage while her companion, Alby, needed to be euthanised.
In an email seen by AAP, Qantas confirmed a greyhound had died while outside its care with the major contributing factor likely "heat stress".
Animal Justice MP Emma Hurst told a NSW parliamentary hearing on Friday under privilege she understood one dog died "after being left on the tarmac for six hours and boiling to death".
NSW Racing Minister David Harris says he will make greyhound racing as safe as he can. (Bianca De Marchi/AAP PHOTOS)
But Greyhound Racing NSW disputes that and "strongly rejects any claim" that two greyhounds were left on the tarmac.
According to the body - based on information provided to it - seven dogs were flown to Dallas Fort Worth Airport on June 18.
The animals arrived at the gate at 4.12pm and were received in the terminal by a transport team at about 5.30pm, it said in a statement on Saturday.
One greyhound had died. A second dog was unwell and taken to a vet around 6.30pm.
"Following expert medical assessment by the veterinarian, it was recommended the dog be euthanised and following consultation it was agreed this was the most humane course of action," Greyhound Racing NSW said.
Necropsy and pathology reports conducted in Dallas were unable to determine a conclusive cause of death.
"However, consulting veterinarians advised the most likely cause was hyperthermia resulting from fluctuations in temperature and humidity," the body said.
Greyhound Racing NSW stressed there was no evidence of dehydration and water was provided.
The five remaining greyhounds were healthy and "are now in loving homes", it added.
NSW Racing Minister David Harris said he only knew of two earlier deaths associated with the US rehoming program, and both occurred prior to crossing the Pacific.
"I'll have to take it on notice, I'm not across the specifics of that," he said on Friday of Ms Hurst's claim made at the inquiry.
"A dog boiling to death isn't a story someone would easily forget," Ms Hurst replied.
Mr Harris later acknowledged he'd received notice of the deaths in June.
He said he was currently negotiating communication improvements with Greyhound Racing NSW.
It comes after the minister was left in the dark about a scathing report on animal welfare breaches by the industry's outgoing chief veterinarian.
The scandal triggered the launching of a snap probe into greyhound racing, starting September 16, to be overseen by the chair of the Greyhound Welfare and Integrity Commission.
Its terms of reference, however, preclude ending racing entirely, a decision defended on Friday by the minister.
The commission's chief executive told the budget estimates hearing his office was unable to oversee the US rehoming program as its powers only covered industry participants.
But he said the commission was closely watching trends in deaths and rehoming.
Greyhound Racing NSW said incidents like the deaths of the two dogs in June are "exceedingly rare in our history of transporting greyhounds by road and aircraft".
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