Magnetoelectric oxide heterostructures are proposed active layers for spintronic memory and logic devices, where information is conveyed through spin transport in the solid state. Incomplete theories of the coupling between local strain, charge, and magnetic order have limited their deployment into new information and communication technologies. In this study, we report direct, local measurements of strain- and charge-mediated magnetization changes in the La_0.7Sr_0.3MnO₃ / PbZr_0.2Ti_0.8O₃ system using spatially-resolved characterization techniques in both real and reciprocal space. Polarized neutron reflectometry reveals a graded magnetization that results from both local structural distortions and interfacial screening of bound surface charge from the adjacent ferroelectric. Density functional theory calculations support the experimental observation that strain locally suppresses the magnetization through a change in the Mn- e_g orbital polarization. We suggest that this local coupling and magnetization suppression may be tuned by controlling the manganite and ferroelectric layer thicknesses, with direct implications for device applications.