One Consumer NZ member lost $14,000 to the scam.
She contacted her bank, ANZ, two days after making the payment but the money had already gone.
Nearly a month on, the victim is waiting to hear the results of police and ANZ investigations.
Consumer NZ chief executive Sue Chetwin said banks needed to be doing more when they became aware of these types of scams.
"ANZ had alerted its staff when its fraud team flagged the problem but an alert on the bank's website was only posted this month," Ms Chetwin says.
The other Consumer NZ member, who fell victim to a similar scam last year, said she was given a goodwill payment of $3300, half the amount she lost, by Kiwibank.
Ms Chetwin said anyone who thinks they've been a victim of this type of scam should report it to police and their bank immediately.