We report an observation of room-temperature magneto-dielectric (RTMD) effect in LaGa0.7Fe0.3O3+γ compound. The contribution of intrinsic/resistive sources in the presently observed RTMD effect was analyzed by measuring direct-current (dc) magnetoresistance (MR) in four-probe geometry and frequency-dependent MR via impedance spectroscopy (MRIS). Present MRIS analysis reveals that at frequencies corresponding to grain contribution (≥1 × 106 Hz for present sample), the observed MD phenomenon is MR-free/intrinsic, whereas at lower probing frequencies (<1 × 106 Hz), the observed MD coupling appears to be MR-dominated possibly due to oxygen excess, that is, due to coexistence of Fe3+ and Fe4+. The magnetostriction is anticipated as a mechanism responsible for MR-free/intrinsic MD coupling, whereas the MR-dominated part is attributed to hopping charge transport along with Maxwell-Wagner and space charge polarization. The multivalence of Fe ions in LaGa0.7Fe0.3O3+γ was validated through iodometric titration and Fe K-edge X-ray absorption near-edge structure measurements. The excess of oxygen, that is, coexistence of Fe3+ and Fe4+, was understood in terms of stability of Fe4+ by means of "bond-valence-sum" analysis and density functional theory-based first-principles calculations. The cation vacancies at La/Ga site (or at La and Ga both) were proposed as the possible origin of excess oxygen in presently studied compound. Present investigation suggests that, to justify the intrinsic/resistive origin of MD phenomenon, frequency-dependent MR measurements are more useful than measuring only dc MR or comparing the trends of magnetic-field-dependent change in dielectric constant and tan δ. Presently studied Fe-doped LaGaO3 can be a candidate for RTMD applications.