Is its offensiveness only slight? (4)
I believe the answer is:
slur
'slight?' is the definition.
(I've seen this before)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for slur that I've seen before include "Pronounce indistinctly - discredit" , "Slight - smear" , "disgrace" , "Innuendo" , "Disparage" .)