Gradient estimates for solutions to parabolic backward equations based on the Laplace operator are well understood. The Laplace operator naturally extends to non-local operators, where a large class of those non-local operators has an intrinsic connection to Lévy processes. The solutions to the corresponding non-local parabolic backward equations are of interest in applications, where the difference to the classical case is that the gradients of the solutions are infinite-dimensional in general. We investigate the singularity properties of those gradients and indicate an application of the obtained estimates.