ImmD clearly made a mistake, and they have now corrected it. You haven't lost anything which was legally yours, so I don't see how you have a case.
If your daughter had actually been resident in HK at any point then you might do, but you made the choice for her to be born and live in New Zealand, and I feel you just need to accept that you perhaps made a mistake, but what is done is done and you need to move on.