Gauge mediated models of supersymmetry breaking often exhibit "gaugino screening," where to leading order in F, gaugino masses are unaffected by higher dimensional Kahler potential interactions between the supersymmetry breaking spurion and the messengers. We provide a derivation of this phenomenon which utilizes the gaugino counterterm originally proposed in the context of anomaly mediation by Dine and Seiberg. We argue that this counterterm is present when there are non-zero messenger F-terms, and can cancel the leading order Feynman diagram contribution to the gaugino mass. We provide a nontrivial check of the regulator independence of our results by performing the computation using both dimensional reduction and Pauli-Villars. This analysis reconciles an apparent contradiction between diagrammatics and analytic continuation into superspace. Show Partial Abstract