The Karlsruhe Tritium Neutrino (KATRIN) experiment aims at measuring the effective electron neutrino mass with a sensitivity of 0.2 eV/c2, i.e., improving on previous measurements by an order of magnitude. Neutrino mass data taking with KATRIN commenced in early 2019, and after only a few weeks of data recording, analysis of these data showed the success of KATRIN, improving on the known neutrino mass limit by a factor of about two. This success very much could be ascribed to the fact that most of the system components met, or even surpassed, the required specifications during long-term operation. Here, we report on the performance of the laser Raman (LARA) monitoring system which provides continuous high-precision information on the gas composition injected into the experiment's windowless gaseous tritium source (WGTS), specifically on its isotopic purity of tritium-one of the key parameters required in the derivation of the electron neutrino mass. The concentrations cx for all six hydrogen isotopologues were monitored simultaneously, with a measurement precision for individual components of the order 10-3 or better throughout the complete KATRIN data taking campaigns to date. From these, the tritium purity, εT, is derived with precision of <10-3 and trueness of <3 × 10-3, being within and surpassing the actual requirements for KATRIN, respectively.