"To say we are outraged is probably rather mild, to be honest we are furious and frustrated," Kurth said.
"We have been given no right of appeal and no right to complain."
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She said the visa application process had been costly, lengthy and highly complex and they were shocked and embarrassed to learn that they had been refused.
Kurth said the five retired friends had undertaken to pay all expenses, including travel fares and visa application costs - and even a bond if required.
Hurst said the group had warmed to both of the men during their one month Ethiopian holiday especially for their attention to detail and going beyond the call of duty in ensuring they had a wonderful holiday.
"We felt compelled to do something as a thank you and after some discussion thought how wonderful it would be to bring them both to New Zealand to experience some Kiwi hospitality and to experience our marvellous country," she said.
"The fact is that these two wonderful young men epitomise everything that one would aspire to be in life and they would never have an opportunity to ever afford such a trip or experience without our offering it as a thank you gift."
Each of the five would fork out about $1500 each, on top of $489 for the visa application and $140 to send their passports to South Africa for INZ verification.
"To add insult to injury, the visa application fee included the new conservation levy of $35...with no indication of refund despite the fact they are not allowed to come," Hurst said.
Hurst said by saying they were non bona fide, INZ were also saying the sponsors aren't bona fide.
"The lack of information and explanation around INZ's decision is shameful, insulting and unacceptable," she added.
Jennie Melville, INZ's acting border and visa operations general manager said the onus was on the applicant to provide sufficient evidence to demonstrate they met immigration instructions.
She confirmed the agency received the two applications on November 22, which were declined a month later, on December 23, 2019.
Melville said the men did not provide sufficient evidence to demonstrate strong employment, financial or family ties in their home country.
"In assessing Abreham and Abenezer's applications, INZ considered their purpose for visiting New Zealand and the fact they were sponsored," she said.
"However, this was not sufficient to demonstrate they met bona fide requirements under immigration instructions."
Melville said after consideration, INZ also felt a bond or grant of limited visa were not warranted in these cases.
"Under the Immigration Act 2009, offshore visitor visa applicants have no appeal rights," she said.
"INZ is happy to speak to [the two men] or their sponsors to ensure they understand immigration instructions."
The sponsors have written to the Immigration Minister seeking intervention.