Fed story back to their studio (7)
I believe the answer is:
atelier
'studio' is the definition.
(atelier is a kind of studio)
'fed story back to their' is the wordplay.
'fed' becomes 'ate' ('eat' can be a synonym of 'feed').
'story' becomes 'lie' (story can mean a fabrication).
'back to' suggests the final letters.
The final letter of 'their' is 'r'.
'ate'+'lie'+'r'='ATELIER'
(Other definitions for atelier that I've seen before include "Designer's workshop" , "Tie earl up in the artist's place" , "I relate to workshop used by artist" , "Artist's workroom" , "Artist's workshop, studio" .)