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Control of magnetization relaxation in magnetic insulators via interfacial spin scattering is demonstrated. The experiments use nanometer-thick yttrium iron garnet (YIG)/Pt layered structures, with the Pt layer biased by an electric voltage. The bias voltage produces a spin current across the Pt thickness. As this current scatters off the YIG surface, it exerts a torque on the YIG surface spins. This torque can reduce or enhance the damping and thereby decrease or increase the ferromagnetic resonance linewidth of the YIG film, depending on the field/current configuration.