Spin waves are promising candidates to carry, transport, and process information. Controlling the propagation characteristics of spin waves in magnetic materials is an essential ingredient for designing spin-wave-based computing architectures. Here, we study the influence of surface inhomogeneities on the spin-wave signals transmitted through thin films. We use micromagnetic simulations to study the spin-wave dynamics in an in-plane magnetized yttrium iron garnet thin film with thickness in the nanometer range in the presence of surface defects in the form of locally introduced uniaxial anisotropies. These defects are used to demonstrate that the backward volume magnetostatic spin waves (BVMSW) are more responsive to backscattering in comparison to magnetostatic surface spin waves (MSSWs). For this particular defect type, the reason for this behavior can be quantitatively related to the difference in the magnon band structures for the two types of spin waves. To demonstrate this, we develop a quasianalytical theory for the scattering process. It shows an excellent agreement with the micromagnetic simulations, sheds light on the backscattering processes, and provides a new way to analyze the spin-wave transmission rates in the presence of surface inhomogeneities in sufficiently thin films, for which the role of exchange energy in the spin wave dynamics is significant. Our study paves the way to designing magnonic logic devices for data processing which rely on a designed control of spin-wave transmission.