  Motivated by discrepancies between recent cold atom experiments and the
associated theory, we explore the effect of immobile holes on the quantum
dynamics of $x$-$z$ spin helices in the one-dimensional $XX$ model. We
calculate the exact spin dynamics by mapping onto a system of non-interacting
fermions, averaging over the distribution of holes. At small hole densities we
find that the helical spin pattern decays exponentially, with a pitch
dependence that agrees with the experiments. At large hole densities we instead
find persistent oscillations. While our analytic approach does not generalize
to the $XXZ$ model with arbitrary anisotropies, we validate a matrix product
state technique which might be used to model the experiments in those settings.
