It's a paragraph border.

On WinWord, you'd select the cell, then choose Borders>Borders & Shading>Apply to:Paragraph>None.



PS: You didn't say anything before about it being applied to the end-of-cell marker of a table cell.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]

Thank you so much! That pesky line is gone.



I had no idea the cell was related to the line (border). I've never seen that sequence of keystrokes to that location before, so I would never have figured it out. I came to the right place!