Y-Messages from previous semesters shouldn't continue as notifications
The only way to get rid of the message notification is to click on the message and read it. There are classes where students will babble about nothing important and the professor will never use this method for important things. If you want to get rid of them, you have to go through all previous semesters and click to view each individual message.
Thank you for your suggestion to improve Learning Suite! Your enhancement request has been added to our ticketing system. Redmine #7497