How do I remove my course from showing up in Google?

If you marked your course as "private" it will not show in Google or any other search engines. Private courses are only visible to those whom you share the URL of the quiz with.

If the course was first public and then marked as private, it's possible that Google indexed it earlier. We add the noindex and nofollow directive for Google (and other search engines) on private quizzes so next time it refreshes, it should remove the quiz from search (a process that can take a few days or can also be done instantly - depends on Google).

If you want it to be removed immediately you can:

Password protect the quiz - So even if someone finds it, they cannot access it without knowing the password. Keep the password simple and common across all quiz takers.
Copy the quiz, mark the copy private and delete the old one. However in this case you would lose quiz taker's data of attempts, reports & stats.

Please also read:
How do I make my courses private?
How is course data and user information protected?