Strip was confused with half of theirs (6)
I believe the answer is:
swathe
'strip' is the definition.
(I've seen this before)
'was confused with half of theirs' is the wordplay.
'confused with' is an anagram indicator.
'half of' suggests halving the letters.
'theirs' cut in half is 'the'.
'was' with its letters anagrammed with 'the' gives 'SWATHE'.
(Other definitions for swathe that I've seen before include "Wrap in bandages - broad mown band" , "Bandage completely - band of mown grass" , "Envelop" , "Cover" , "Wrap in several layers" .)