<p>This study investigates the potential effect of accidental coincidences on the selection of Birks' ionization quenching parameter (<i>kB</i>) in triple-to-double coincidence ratio (TDCR) measurements, performed with efficiency variation using grey filters. A retrospective analysis was conducted on previous determinations of the <i>kB</i> value in TDCR measurements, both with and without corrections for accidental coincidences. Our analysis demonstrates that there are variations in the determined <i>kB</i> value, which are not connected to the correction for accidental coincidences and the origin of which is currently unknown. For a given sample, the determined <i>kB</i> value varies between different TDCR counting systems. For a given system, the determined <i>kB</i> value varies between different radionuclides and shows dependence on the coincidence resolving time. Compared to these variations, the effect of applying the correction for accidental coincidences is small and remains within the estimated statistical uncertainties. In this sense the results of this work validate the selections of <i>kB</i> parameters made in past experiments, where corrections for accidental coincidences were not available. However, it is important to note that these results do not suggest disregarding the correction for accidental coincidences, it is essential and has to be applied. The results of this study suggest that further theoretical and experimental efforts are needed to better understand the modelling of ionization quenching within the TDCR model.</p>