Discourtesy is acting in a rude or thoughtless way. If you yell orders at your restaurant server and leave him a small tip, you're treating him with extreme discourtesy.
The noun discourtesy is a formal way to say "rudeness" or "disrespect." Cutting in line, interrupting others, chewing with your mouth wide open, being late for an important meeting — these are all examples of discourtesy. Courtesy means "elegance of manners" or "politeness," from a root meaning "courtly manners." When you add the prefix dis-, "the opposite of," you get discourtesy.