FAQ for
Secretary (2002) More at IMDbPro »

A worm is a dirty, inappropriate thing to find in a business letter (or any letter for that matter) and therefore deeply annoys Mr. Grey, who hates anything to be dirty or out of place. It's a "mistake", which is why he circles it in red. Lee intends it to get him upset so as to draw punishment, which of course it does. It has also been suggested that a worm could be symbolic of a limp male member and could therefore be construed as an attack on his manhood, but if so the end result would be the same (namely, provoking him).