Based upon this there could well exist the possibility the phone does have a 3rd party screen - installed when you got the replacement phone.
I'd be straight to the disputes tribunal lodging action claiming they supplied you with a replacement phone that had fake parts. It's up to them to prove they didn't.
As they purchased it in OZ, would they be covered by the DT in NZ? I mean , who do they have the contract with and are actually taking to the DT? If it is Apple, wouldn't it be Apple Australia?
It's the NZ repair centre that repaired it (and replaced it) therefore I don't see any reason why you couldn't take lodge a claim against them.