JandM,
No, there is no fee required to be paid for a character waiver. There is a specific formula for gaining a character waiver in the policy.
A5.25.1 Action
An immigration officer must not automatically decline residence class visa applications on character grounds.
An immigration officer must consider the surrounding circumstances of the application to decide whether or not they are compelling enough to justify waiving the good character requirement. The circumstances include but are not limited to the following factors as appropriate:
if applicable, the seriousness of the offence (generally indicated by the term of imprisonment or size of the fine);
whether there is more than one offence;
how long ago the relevant event occurred;
whether the applicant has any immediate family lawfully and permanently in New Zealand;
whether the applicant has some strong emotional or physical tie to New Zealand;
whether the applicant's potential contribution to New Zealand will be significant.