According to our good friend Matua Kahurangi this is initiated by The Maori Party.
Here is a link to his full post.
https://matuakahurangi.com/p/te-pati-maori-rages-over-fbi-office
My Guess:
They will struggle to get 10,000 signatures.
Here Is A Petition I Definitely Will Not Be Signing.
No Minister 
Of course the will get over 10,000 signatures PDM!
Probably get over 20,000. Just use the same methodology they used for Treaty Principles Bill submissions!
Assuming this is true (it could be bullshit for all I know), I’m not sure what the problem is. Any New Zealand resident investigated and prosecuted for US Federal crimes will still have to be extradited with permission from the New Zealand justice system. It’s not like the FBI can just kidnap NZ citizens Eichmann style.
You have faith in the NZ justice system? Where did you get that, at a flea market? And why would you trust he FBI not to abuse their powers?
FBI = Famous But Incompetent.
I have little faith in either institution, but it nonetheless would be unlikely that the FBI would operate in a friendly foreign country extrajudicially. That’s the CIA’s job. The FBI are concerned with criminal activity under US Federal law, which would be unlikely to impinge on the rights of New Zealanders, unless they were pedos, terrorists or gangsters. In which case sane individuals ought to welcome their removal from New Zealand to face justice.
Goodness exiled are you sure about your last sentence?
Our 54 year old daughter is visiting and she seems to be of the opinion that what you say won’t happen is the purpose of the FBI office in NZ.
If she stumbles across it she will certainly be signing the petition. What is more worrying is there are other obviously/supposedly intelligent, middle aged women who believe the same.
I know nothing about this other than what is alleged. I do know that the job of the FBI is to police US Federal law. Presumably there are people in New Zealand violating US Federal law sufficient for them to have an office here. But the FBI has no legal status in New Zealand, so they would have to work with the NZ police to arrest anyone. TPM has yet to show the FBI has been granted any jurisdiction in this regard.