To remove the shared mailbox from your Outlook desktop app, perform the following steps depending on which version of Outlook you are using.
New Outlook for Desktop on Windows
Coming shortly...
Classic (Legacy) Outlook for Desktop on Windows
- In Outlook, click on File, and then click the Account Settings drop down, and select the Account Settings option.

- In the Account Settings box, click the account you wish to remove, and hit the "Remove" button.

- Confirm that you wish to remove the account by clicking yes.

- The account and associated data files on your computer will be removed.