Hi @efudge,
The ability to see and use the import functionality is tied to the "Course Content - add" permission according to the Canvas Course Role Permissions documentation. For your needs, that's problematic because I'm pretty confident you don't want to prevent teachers from adding content completely, just not by using the import tool, correct?"
Since a permission change is probably out of the question here, that leaves you with the option to use custom javascript/css via editing your Canvas theme. The problem with this method is that you're really only hiding things, not blocking the functionality from being used. Savvy users can easily work around restrictions like this if they really want to, but I don't know how much of an issue that would be for you. If you do go down this road, it would be good to know whether you want to block all import functionality (even importing from another existing course in your instance), or if you're just trying to block imports of common cartridge files or something else. Depending on your needs, the code may be relatively simple or get complex pretty quickly. I have hidden other buttons on the course settings page with this method, so it's definitely doable if you're willing to go to this level.
Please do respond back here with more details if you're able!
-Chris