Nanostructured magnetic materials provide an efficient tool for light manipulation on sub-nanosecond and sub-micron scales, and allow for the observation of the novel effects which are fundamentally impossible in smooth films. For many cases of practical importance, it is vital to observe the magneto-optical intensity modulation in a dual-polarization regime. However, the nanostructures reported on up to date usually utilize a transverse Kerr effect and thus provide light modulation only for p-polarized light. We present a concept of a transparent magnetic metasurface to solve this problem, and demonstrate a novel mechanism for magneto-optical modulation. A 2D array of bismuth-substituted iron-garnet nanopillars on an ultrathin iron-garnet slab forms a metasurface supporting quasi-waveguide mode excitation. In contrast to plasmonic structures, the all-dielectric magnetic metasurface is shown to exhibit much higher transparency and superior quality-factor resonances, followed by a multifold increase in light intensity modulation. The existence of a wide variety of excited mode types allows for advanced light control: transmittance of both p- and s-polarized illumination becomes sensitive to the medium magnetization, something that is fundamentally impossible in smooth magnetic films. The proposed metasurface is very promising for sensing, magnetometry and light modulation applications.