Hi Lindsay,
What word has actually done is put a border at the bottom of the paragraph
to give you the line.
Put the cursor immediatly above the line,
and do (from the menu)
Format -> Borders and Shading.
Select 'None' as the type of border and press OK.
Note this is for Word2000, another version might be slightly different, but
the principle will be the same...
;-)
Cheers,
Chris.