Soft material picked up (4)
I believe the answer is:
felt
I believe this is a double definition.
'soft material' is the first definition.
'picked up' is the second definition.
('feel' can be a synonym of 'pick up')
(Other definitions for felt that I've seen before include "Sensed - beret material" , "hat-maker" , "checked by hand" , "Was aware of; a fabric" , "suitable for a fedora" .)