The KATRIN experiment is designed for a direct and model-independent determination of the effective electron anti-neutrino mass via a high-precision measurement of the tritium -decay endpoint region with a sensitivity on of 0.2  (90% CL). For this purpose, the -electrons from a high-luminosity windowless gaseous tritium source traversing an electrostatic retarding spectrometer are counted to obtain an integral spectrum around the endpoint energy of 18.6 keV. A dominant systematic effect of the response of the experimental setup is the energy loss of -electrons from elastic and inelastic scattering off tritium molecules within the source. We determined the energy-loss function in-situ with a pulsed angular-selective and monoenergetic photoelectron source at various tritium-source densities. The data was recorded in integral and differential modes; the latter was achieved by using a novel time-of-flight technique. We developed a semi-empirical parametrization for the energy-loss function for the scattering of 18.6-keV electrons from hydrogen isotopologs. This model was fit to measurement data with a 95% gas mixture at 30 K, as used in the first KATRIN neutrino-mass analyses, as well as a gas mixture of 96% purity used in KATRIN commissioning runs. The achieved precision on the energy-loss function has abated the corresponding uncertainty of [1] in the KATRIN neutrino-mass measurement to a subdominant level.