Fun fact: this episode is supposed to be in 2266. That last Irish King (discounting the invading Anglo-Normans) was around 1170. That's 1096 years. Assuming 25 years per generation, that's 43.84 generations.
It is possible to use no soap and still be clean. That is not a dirtiness. That is water. Even in the dirtiest circumstances, there is always a soap- sometimes only a bubble. Trust that soap. Scrub a way back, no matter what it takes.
Or