Hello, @X-Box-11-2021,
Welcome to the Microsoft Q&A platform!
Firstly, I'll answer the question in your title. The ExchangePublishedUser is an externally shared calendar that is followed by an indication of which address it is published to.
Secondly, the reason they are still listed in the calendar permissions list is because they are legacy entries from when the calendar was shared externally, and they may still exist even if the account in question is no longer active.
Finally, you can use PowerShell to remove these inactive accounts from the calendar permissions list just as you delete a normal account. Below are the commands you will need to use as well as a test screenshot:
Commands of deletion:
Remove-MailboxFolderPermission -Identity "******@company.com:\Calendar" -User "******@company.com"
Remove-MailboxFolderPermission -Identity "******@company.com:\Calendar" -User "******@company.com"
Test results:
(Note: The ******@company.com in the screenshot represents the ******@company.com you want to delete, the deletion operation is the same for both.)
If the answer is helpful please click on ACCEPT ANSWER as it could help other members of the Microsoft Q&A community who have similar questions and are looking for solutions.
Thank you for your support and understanding.
Best Wishes,
Alex Zhang