In recent years, graphene field-effect-transistors (GFETs) have demonstrated an outstanding potential for terahertz (THz)photodetection due to their fast response and high-sensitivity. Such features are essential to enable emerging THz applications,including 6G wireless communications, quantum information, bioimaging and security. However, the overall performance of these photodetectors may be utterly compromised by the impact of internal resistances presented in the device, so-called access or parasitic resistances. In this work, we provide a detailed study of the influence of internal device resistances in the photoresponse of high-mobility dual-gate GFET detectors. Such dual-gate architectures allow us to fine tune (decrease)the internal resistance of the device by an order of magnitude and consequently demonstrate an improved responsivity and noise-equivalent-power values of the photodetector, respectively. Our results can be well understood by a series resistance model, as shown by the excellent agreement found between the experimental data and theoretical calculations. These findings are therefore relevant to understand and improve the overall performance of existing high-mobility graphene photodetectors.