A family of Microsoft word processing software products for creating web, email, and print documents.
Got it fixed. Later changes to the document ended up causing the same problems in all of my tables, not just one.
But, we figured out how to fix it, even if we still don't understand what caused the problem.
The problem was that each paragraph within the tables had it's own border applied separate from the cell border of the table. I ended up having to place the cursor in the text of a cell, then click on the Borders icon, pick the top border or bottom border as applicable. But I had to click the top or bottom border TWICE for each paragraph to get the offending line to disappear. Hitting it a third time caused the border of the table cell to disappear also, so I did not do that. Unfortunately, I had to do this to every cell individually, one at a time, once for the top and again for the bottom. Tedious, but it cleaned up the problem