As the research on magnetostatic surface spin waves (MSSWs) gains momentum, a concrete understanding of how these waves behave at interfaces is still undeveloped. In this work, we theoretically investigate how a MSSW traveling in a ferromagnetic film scatters across a sharp step of magnetic parameters in the film such as the applied field. An integral equation is derived, which describes the scattering process. We solve this equation both directly numerically and using a second Born approximation. We find that scattering produces partial reflection and partial transmission of the wave through the step. A nontrivial behavior of the amplitude of the transmitted wave as a function of the step size is observed in the calculation and analyzed.