Document understanding templates are not saved while pushing the project to repository

I have created a taxonomy with a couple of document types and extractor with tempates for those types. However, when I push changes to GIT, templates are saved without original documents with marked fields. When I clone the repository to another machine, I can see templates in Template manager, but cannot edit them/change/mark fields (there is no “Edit” option, only “Delete”). For that I have to manually export templates and save them in a separate folder.

Is there any way to push templates to repository together with original documents?