Determining the exact pairing symmetry of the superconducting order parameter in candidate unconventional superconductors remains an important challenge. Recently, a new method, based on phase sensitive quasiparticle interference measurements, was developed to identify gap sign changes in isotropic multiband systems. Here we extend this approach to the single-band and multiband nodal d-wave superconducting cases relevant, respectively, for the cuprates and likely for the infinite-layer nickelate superconductors. Combining analytical and numerical calculations, we show that the antisymmetrized correction to the tunneling density of states due to nonmagnetic impurities in the Born limit and at intermediate-scattering strength shows characteristic features for sign-changing and sign-preserving scattering wave vectors, as well as for the momentum-integrated quantity. Furthermore, using a realistic approach accounting for the Wannier orbitals, we model scanning tunneling microscopy data of Bi2Sr2CaCu2O8+δ, which should allow the comparison of our theory with experimental data. © 2020 American Physical Society.