besmear
Coat with grime
To besmear is to smear something over a surface, or to smear a surface with something—usually something messy or unpleasant: The child besmeared the walls with chocolate.
The word is literary and old-fashioned, rarely encountered outside historical texts.
Figuratively, to besmear can mean to sully a reputation.
spread
To distribute widely
anoint · cover · rub · apply · lather · cake · layer · bedaub · smudge · streak
smudge
Unclear dirty mark
grime · filth · splatter · blot · spot · streak · defile · contaminate · pollute · taint
slander
Spoken false defamation
denigrate · malign · calumniate · disparage · blacken · impugn · traduce · asperse · discredit · denounce