In this article, we present a general construction of Lyapunov-Krasovskii functionals for a class of neutral-type time delay systems with a linear difference part and homogeneous right-hand sides of degree strictly greater than one. Under an assumption that the corresponding difference matrix equation as well as a system with zero delays are asymptotically stable, the functionals allow proving delay-independent asymptotic stability. They are based on the Lyapunov functions of the corresponding delay free systems and constitute a generalization of constructions presented recently for homogeneous systems of retarded type. The functionals are applied to the robustness analysis with respect to uncertainties at the right-hand sides and at the difference term as well.