Reportedly influenced fabric (5)
I believe the answer is:
suede
'fabric' is the definition.
(I know that suede is a type of fabric)
'reportedly influenced' is the wordplay.
'reportedly' shows a homophone (sound like).
'influenced' becomes 'swayed' (swaying is a kind of influencing).
'swayed' sounds like 'SUEDE'.
(Other definitions for suede that I've seen before include "unprepared material" , "Soft goatskin" , "Undressed leather" , "leather material" , "Soft leather with one side napped" .)