Inch taken off bird’s rib (5)
I believe the answer is:
chaff
'rib' is the definition.
(thesaurus)
I don't understand how the remainder of the clue works.
(Other definitions for chaff that I've seen before include "Light banter - husks from corn" , "Winnowed husks of grain" , "Worthless material (from corn)" , "Corn husks - worthless stuff" , "twit" .)