You could use the assignment “remind me to grade by” date or use the “cut-off date” plus two weeks. This means the course will still appear as a current course for every student until every student has submitted, resubmitted and been marked. But Moodle is making use of the course end date so that students can list their 'current courses' on the the dashboard among other places. This means that the course end date must be set in Moodle to be after all work has been submitted and marked including any extensions (very common in Covid times) and including any resits. This cannot be overridden in any way except changing the course end date.
If I understand correctly this means that whatever is set as the end date for courses in Moodle will be the date when the class in Turnitin expires and therefore the date by which all marking must be completed. We have just been caught out by the change in how Turnitin sets the expiry date (Turnitin Support Case 01908416).
