The combination of ferromagnets with topological superconductors or insulators allows for new phases of matter that support excitations such as chiral edge modes and Majorana fermions. EuS, a wide-bandgap ferromagnetic insulator with a Curie temperature around 16 K, and SrTiO3 (STO), an important substrate for engineering heterostructures, may support these phases. We present scanning superconducting quantum interference device measurements of EuS grown epitaxially on STO that reveal micron-scale variations in ferromagnetism and paramagnetism. These variations are oriented along the STO crystal axes and only change their configuration upon thermal cycling above the STO cubic-to-tetragonal structural transition temperature at 105 K, indicating that the observed magnetic features are due to coupling between EuS and the STO tetragonal structure. We speculate that the STO tetragonal distortions may strain the EuS, altering the magnetic anisotropy on a micron scale. This result demonstrates that local variation in the induced magnetic order from EuS grown on STO needs to be considered when engineering new phases of matter that require spatially homogeneous exchange.