An anomalous optical second-harmonic generation (SHG) signal was previously reported in Sr₂IrO₄ and attributed to a hidden odd-parity bulk magnetic state. We investigated the SHG signal using magnetic-field-dependent SHG rotational anisotropy and wide-field SHG imaging combined with atomic force microscopy. We observe a two-fold rotational symmetry of the anomalous SHG signal as a function of in-plane magnetic field orientation that is associated with a crystallographic distortion. We also show a change in SHG signal across step edges that tracks the bulk antiferromagnetic stacking pattern. We will discuss the implications of these results for the origin of the anomalous SHG signal.