It is well known that the induced linear tidal response of Schwarzschild black holes, as opposed to other types of astrophysical compact objects, is exactly zero in general relativity. I will discuss the role of nonlinearities in the calculation of the tidal response of black holes beyond linear order. After solving the static nonlinear Einstein equations for the perturbations, I will explicitly perform the matching with the point-particle effective theory and show that the tidal deformability remains zero at higher order in perturbation theory.