Cox's Black Box

For the last couple of years, there is a black box with a label of:  "Cox", which appears in the lower left corner of my desktop screen, when I open Microsoft Outlook.

The box has e-mail addresses [wrong, bad or defective] of  e-mails that were not delivered.  Attempts to delete these e-mail addresses are unsuccessful.

How do I delete the the addresses in the box, or the box?

Thanks.