Earlier quoted context omitted.
You filter out the other elements, and release the water. Water pretty much can't get radioactive. (For more than a few minutes.) The longest radioactive oxygen you can make in a reactor has a half life of 26 seconds. For hydrogen, deuterium is not radioactive, and tritium can't be made in a light water reactor. So water effectively can't get radioactive.
And they have these filters right there, handy and ready to use just in case they started pumping in sea water?
The water is being boiled away, not circulated with pumps.