thoroughly, completely, become clear
澈 centers on thoroughness and clarity: doing something completely, or becoming clear and transparent. The idea of water-like purity connects the senses of thoroughness and clarity.
澈 combines 氵 (water) with a phonetic component that also appears in 徹 and 撤. The water radical suggests clarity or washing away impurities, while the phonetic likely contributed the reading and the idea of thoroughness.
Water 氵 on the left flows through the right side, washing everything until it is thoroughly clean and clear. Picture a stream making a muddy stone completely transparent.
For テツ, imagine a clear, thorough test of water purity: test -> テツ, and the water becomes completely clear.