>According to https://answers.microsoft.com/en-us/msoffice/forum/all/clear-new-mail-alert-in-taskbar-icon-when-mail-is/31085b01-b5cd-454c-b011-2724dec1eb93?tab=AllReplies#tabs , this was happening with Outlook 2016 at one point. The fix apparently was to update Office.
>
>That thread is 2 years old and is for Outlook 2016 but it might be worth trying in your case.

In Outlook/File/Office Account, the Office Updates was indicating Updates are automatically downloaded and installed.

When I clicked on Update Options, I selected Update Now. Surprisingly, it started to download some stuff and installed. Not sure why the automatic option did not do its job. Apparently, it might not do major updates.

The situation remains.

Here is a more details scenario:

1. Go in Outlook
2. Send an email to yourself
3. Minimize Outlook
4. Wait for the yellow enveloppe to appear in the tray
5. Use iPhone
6. Go in Mail
7. Click on the inbox
8. At this time, the new mail should be seen as unread
9. Click on it
10. Click Back
11. The mail is now showing as read
12. Delete it
13. Click on Outlook
14. The mail is not showing as it was deleted on iPhone
15. The yellow enveloppe is still showing

The only way to remove the enveloppe is to restart Outlook.