If it is horizontal or vertical (rather than diagonal), it may well be a
paragraph border. Even if the cell itself does not have borders, the text
might. Select the text and press Ctrl+Q for a start. If that removes the
border but also removes formatting you do not want to lose, or if it does not
work, click the Borders button in the Paragraph group on the Home tab to
drop down the menu and choose No Border.
I have a table, and a cell contains a line in it, which I cannot copy
and paste, or format copy and paste, or delete, or move, or select.
Any idea what this line is, and how I can move it, delete it etc?
This is a Word 2003 document opened in Word 2007.