Interaction of magnetic metasurfaces with common magnetic dielectrics is of high interest from both the fundamental and practical points of view. Control over the magnetic domain structure of magneto-optical materials is of principal importance for a number of applications. Interaction of garnets with overlying ferromagnetic structures can provide an additional avenue for the domain manipulation. In this study, we demonstrate that ferromagnetic Co/Au gratings on the surface of rare-earth-substituted iron garnet films have a strong influence on the orientation and width of the stripe domains (SDs), as revealed by optical microscopy and magneto-optical studies. Namely, we show (i) a tendency of the SDs alignment along the Co/Au stripes that are turned by 5∘–20∘ from the direction of the external magnetic field and (ii) plateaulike dependencies of the SDs’ width on the field strength, which are not specific for pristine garnet. The key mechanism here is the magnetostatic interaction of the ferromagnetic stripes and the garnet surface, which allowed us to tame the domain structure and to fix their in-plane position. These findings allow us to overcome the chaotic domains orientation and thus increase the stability of magneto-optical devices.