My university has a lab with monitored computers for exams which I use, and should help stop students from installing extensions. At the same time, if I catch someone managing to use it, I don't think the conduct office would care enough to even allow me to lower their grades, so it's more of a security theater.
Some universities may use locked browsers, such as LockDown Browser. I don't have any experience with it and don't know if it stops specifically this extension, but I believe it should.
I guess an admin could experiment with changing some of the things it probably looks for in the quiz page's HTML. An instructor could also try making the quiz less readable for a scraper, but that might also break screen readers.