The first of three $116 instalments was paid yesterday to two million New Zealand tax residents who earn under $70,000.
But questions are being raised if it does enough to close the gap with the rising cost of living in New Zealand, while many overseas are believed to have got the payment too.
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Salvation Army senior policy analyst Paul Barber said since the pandemic began there was a group of people struggling to get by.
He told Morning Report he hoped the payment would help people.
However, "most of the people that the Salvation Army works for, and supports are not actually eligible for this cost of living payment as they are relying on welfare benefits".
"We are disappointed that this additional payment didn't also go to the 345,000 people who are relying on welfare, who had the lowest incomes ... they're just as hard hit by the cost pressures and in greater need in many ways."
Barber said high rent too was eating up much of people's income and more needed to be done for those on lower incomes.
The government does not know exactly how many ineligible people have received the cost of living payment.
National Party deputy leader Nicola Willis told First Up she was trying to find out how many people overseas were receiving the cost of living payments.
"I've been inundated by messages from people around the world who have received the payment, who didn't expect it, didn't want it, and quite frankly are embarrassed that they have received it.
"In some cases, they haven't lived in New Zealand for as many as six or seven years.
"The only thing these people seem to have in common is that they have a dormant New Zealand bank account and that they once had an IRD number ... and once even if many moons ago paid tax here."
She said some were on short-term working visas and left years ago.
"I will be asking questions in Parliament this week about it because my concern is that this muck-up is bigger than ministers think."
