How to import specific terms using Zotero Integration?

You missed the Data explorer feature (cmd / ctrl + P -> Search 'Data explorer'), which is a great feature of Zotero Integration (Templating documentation link).

Data explorer lets you explore all the data associated with Zotero items, and see how it is structured. It also lets you preview your templates as you edit them.

And you can even copy-paste fields from data explorer into your template.