Their Customer Services Team is a bit thick.
I got this follow up response:
Thank you for contacting Audible!
Amazon is required to charge and remit New Zealand GST based on the information provided by customers at the time an order is placed. At the time the New Zealand GST was collected, Amazon determined you were a New Zealand resident. Amazon cannot refund New Zealand GST without a valid New Zealand GST registration number.
In accordance with New Zealand GST legislation that subjects remote services to tax, Audible is required to charge GST on cross-border supplies of remote services to customers located in New Zealand as of October 1, 2016. Unless a customer has provided their GST registration number Amazon will collect and remit New Zealand GST at a standard rate of 15% from residents of New Zealand. New Zealand customers who provide Amazon with their GST registration number will not have a GST of 15% applied to their purchases.
We are sorry for any inconvenience this may have caused. Thank you for your patience for this matter
Thank you again for contacting Audible. If you would like additional assistance, please do not hesitate to contact us. We are here to help 24 hours a day, 7 days a week.