Q: How do I remove people from receiving a notification every time a student completes a quiz / assessment?
A: If it is just an email notification about an assessment module being completed (rather than an entire course) then you need to go in and update your assessment notification settings by going to the course as an admin (via Courses tab), then click in to the assessment module, and then go to the "Alerts" tab. Click the gray X to the right of the individual's name to remove them from the alert list. You will also need to check the settings tab to make sure the 'Notification Email' at the bottom is correct or you can un-check the box completely.
We built out a course all around creating Assessments in Litmos, check it out here: How To: Create an Assessment