Hi @GlennWatson,
I have found the following info in the admin guide around grading periods, which I think provides at least a bit of an explanation for the behavior you're encountering:
Close Dates
You can also add a close date to grading periods, which allows you to extend the time that instructors can edit grades after the grading period has ended. By default, the close date is the same as the end date. However, the close date can be edited to any date after the end date.
At the course level, Canvas validates assignments against closed grading periods in Canvas. Canvas validates assignments against closed grading periods in the Gradebook and SpeedGrader and various settings and options in the Assignments, Discussions, and Quizzes feature areas. For each grading period, the close date is the same as the end date, unless the close date is changed by an admin. Instructors cannot edit any assignments with due dates in a closed grading period.
With the above in mind, and the message you're getting, I'm guessing the close date was before today (or whenever you first tried to delete the quiz). While your admin team could change the close date for the grading period, it's likely they have things set up as part of a system/process for transferring finalized grades back into your school's official gradekeeping system (likely some sort of student information system). Even though you may have good reason for wanting to delete the quiz, it could cause grade discrepancies which could lead to other issues down the road...
At least form my interpretation, Canvas allows for as much openness as your school admins want to give. In this case, it seems your admins want less openness than you'd like. Since it's not really a Canvas issue, I would advise you to talk to your school's Canvas team, even though you may not want to. They would ultimately be the ones that could change Canvas settings or at least provide the exact explanation for why the settings are how they are.
I hope this info helps a bit.
-Chris
