We study repetitions in infinite words coding exchange of three intervals with permutation (3,2,1), called 3iet words. The language of such words is determined by two parameters $varepsilon,ell$. We show that finiteness of the index of 3iet words is equivalent to boundedness of the coefficients of the continued fraction of $varepsilon$. In this case we also give an upper and lower estimate on the index of the corresponding 3iet word.
