Apparently, this appears to be a bug.

1. Receive a new Outlook message
2. At that time, the yellow enveloppe is shown, indicating a new message received
3. Check that message on iPhone
4. At that time, the yellow enveloppe remains even if I read it on iPhone
5. Check Outlook inbox and see that the message is however no longer shown as unread
6. From there, no matter what you do, the enveloppe remains and we can no longer benefit of that visual effect to know if upcoming new emails have arrived