The superconductor TmNi₂B₂C possesses a significant fourfold basal plane anisotropy, leading to a square vortex lattice (VL) at intermediate fields. However, unlike other members of the borocarbide superconductors, the anisotropy in TmNi₂B₂C appears to decrease with increasing field, evident by a reentrance of the square VL phase. We have used small-angle neutron scattering measurements of the VL to study the field dependence of the anisotropy. Our results provide a direct, quantitative measurement of the decreasing anisotropy. We attribute this reduction of the basal plane anisotropy to the strong Pauli paramagnetic effects observed in TmNi₂B₂C and the resulting expansion of vortex cores near H_c2.