In this work, we investigate the structural and dynamic magnetic properties of yttrium iron garnet (YIG) films grown onto gadolinium gallium garnet (GGG) substrates with thin platinum, iridium, and gold spacer layers. Separation of the YIG film from the GGG substrate by a metal film strongly affects the crystalline structure of YIG and its magnetic damping. Despite the presence of structural defects, however, the YIG films exhibit a clear ferromagnetic resonance response. The ability to tune the magnetic damping without substantial changes to magnetization offers attractive prospects for the design of complex spin-wave conduits. We show that the insertion of a 1-nm-thick metal layer between YIG and GGG already increases the effective damping parameter enough to efficiently absorb spin waves. This bilayer structure can therefore be utilized for magnonic waveguide termination. Investigating the dispersionless propagation of spin-wave packets, we demonstrate that a damping unit consisting of the YIG/metal bilayers can dissipate incident spin-wave signals with reflection coefficient R < 0.1 at a distance comparable to the spatial width of the wave packet.