Material reportedly moved to and fro (6)
I believe the answer is:
swayed
'moved to and fro' is the definition.
'swayed' can be an answer for 'moved' (swaying is a kind of moving). I'm unsure of the 'to and fro' bit.
'material reportedly' is the wordplay.
'material' becomes 'suede' (suede is a kind of material).
'reportedly' indicates a 'sounds like' (homophone) clue.
'suede' sounds like 'SWAYED'.
Can you help me to learn more?
(Other definitions for swayed that I've seen before include "lacked stability" , "Ruled; influenced" , "was unsteady on one's feet" , "Brought round" , "Being under the influence" .)