I agree the booking fees are a rip off and I find the agents are insistent on charging them even to Elite Air NZ members. If I were you I'd grab evidence (screenshots from Google Flights & Air NZ website) and make a formal complaint to try get refunded for the contact centre fees. You booked through them because the website doesn't show the cheapest fare.
I honestly wonder how much people are getting overcharged through the website as I've come across this myself a few times.