We study the linear and nonlinear optical properties of hybrid metallic–dielectric plasmonic gap nanoantennas. Using a two-step-aligned electron beam lithography process, we demonstrate the ability to selectively and reproducibly fill the gap region of nanoantennas with dielectric nanoparticles made of lithium niobate (LiNbO3) with high efficiency. The linear optical properties of the antennas are modified due to the large refractive index of the material. This leads to a change in the coupling strength as well as an increase of the effective refractive index of the surrounding. The combination of these two effects causes a red- or blue-shift of the plasmonic modes, respectively. We find that the nonlinear optical properties of the combined system are only modified in the range of one order of magnitude. The observed changes in our experiments in the nonlinear emission can be traced to the changed dielectric environment and thus the modified linear optical properties. The intrinsic nonlinearity of the dielectric used is in fact small when compared to the nonlinearity of the metallic part of the hybrid antennas. Thus, the nonlinear signals generated by the antenna itself are dominant in our experiments. We demonstrate that the well-known nonlinear response of bulk dielectric materials cannot always straightforwardly be used to boost the nonlinear response of nanoscale antenna systems. Our results significantly deepen the understanding of these interesting hybrid systems and offer important guidelines for the design of nanoscale, nonlinear light sources.