High-frequency gravitational waves (f≳1 MHz) may provide a unique signature for the existence of exotic physics. The lack of current and future gravitational-wave experiments sensitive at those frequencies leads to the need of employing different indirect techniques. Notably, one of the most promising ones is constituted by graviton-photon conversions in magnetic fields. In this work, we focus on conversions of a gravitational-wave background into photons inside the Milky Way magnetic field, taking into account the state-of-the-art models for both regular and turbulent components. We discuss how graviton-to-photon conversions may lead to imprints in the cosmic photon background spectrum in the range of frequencies f∼109-1026 Hz, where the observed photon flux is widely explained by astrophysics emission models. Hence, the absence of any significant evidence for a diffuse photon flux induced by graviton-photon conversions allows us to set stringent constraints on the gravitational-wave strain hc, strengthening current astrophysical bounds by ∼1-2 orders of magnitude in the whole range of frequencies considered.