We show that the propagating modes in a strongly-guided chiral one-way photonic crystal are not backscattering-immune even though they are indeed insensitive to many kinds of scatters. Since these modes are not protected by the nonreciprocity, the backscattering does occur under certain circumstances. We use a perturbative method to derive criteria for the prominent backscattering in such chiral structures. From both our theory and numerical examinations, we find that the amount of backscattering critically depends on the symmetry of scatters. Additionally, for these chiral photonic modes, disturbances at the most intense parts of field profiles do not necessarily lead to the most effective backscattering.