Hi Justin
Probably the easiest way to eliminate these cross references is to ask your programmer to put all links as relative links rather than as absolute links. Relative links have the disadvantage that they can generate endless loops if something is wrong with the HTML - but this is something you can easily check with Screaming Frog.
If you check the .com version - example https://www.zenory.com/blog/tag/love/ -it's calling zenory.co.nz for plenty of links (just check the source & search for .co.nz) - both the http & the https version
You can check all these pages by hand - but I guess your programmer must be able to do this in an automated way.
It is also the case the other way round- on the .co.nz version - you'll find references in the source to the .com version
In screaming frog - the links with "NZ" are the only ones which should stay absolute - as they point to the other version
Hope this clarifies
Dirk