I have an Exchange mailbox with several other mailboxes that it has full permissions on.
Exhange 2010 or 2013, I don’t remember which, added a feature that adds the mailboxes to Outlook automatically.
So, instead of having to go to account settings and navigating to advanced settings and manually adding additional mailboxes to open it does it for you.

That’s great except when you don’t want them to or when you remove the full access permissions and it decides to stay in Outlook.

To remove a mailbox that keeps showing up even though you’ve removed the Full access permissions.  Open Active Directory Users and Computers find the users account.  Click on Attribute Editor.  Scroll down the list until you find msExchDelegateListLink and remove the user account you don’t want the mailbox showing up in.

You can also turn off Exchange auto mapping on individual accounts.
This will give Administrator full access on the TheUser account without automatically adding it to Outlook:
(so you will have to manually add the account in account settings, open these additional mailboxes)

Add-MailboxPermission -Identity TheUser -User ‘Administrator’ -AccessRight FullAccess -InheritanceType All -Automapping $false