Minor shows discourtesy (6)
I believe the answer is:
slight
I believe this is a double definition.
'minor' is the first definition.
(I've seen this before)
'discourtesy' is the second definition.
(I know that slight is a type of discourtesy)
'shows' is the link.
(Other definitions for slight that I've seen before include "cut" , "Deliberate rebuff" , "A rudeness; feeble" , "Minor - offence" , "Put down" .)