I object quietly to the woven fabric (4)
I believe the answer is:
mesh
'the woven fabric' is the definition.
(I've seen this in another clue)
'i object quietly' is the wordplay.
'i object' becomes 'me' ().
'quietly' becomes 'sh'.
'me'+'sh'='MESH'
'to' acts as a link.
(Other definitions for mesh that I've seen before include "Net fabric" , "Entangle, entwine" , "Undeviating" , "Net, snare" , "Open fabric" .)