I agree with the idea that what's probably happening is that the filter is removing some radioactive dust. It cannot remove radiation per se, but if the dust is the big problem then it might help a lot.

If the only problem is dust contamination, you don't necessarily need a professional filter (though that helps). You could strain water thru several layers of very fine cloth, or better still through some of those large filter papers that chemists use when they do experiments. You just need to filter the water to some sub-micron level. However, if the process takes a long time that may be frustrating.

On the other hand, if the water contains dissolved materials that are radioactive - then you've got a problem. A filter won't get out dissolved materials - you would need to evaporate the water to clean it in that case.

Do you own a Geiger counter that could even measure the radioactivity from water? I don't have one, and I wonder how many people actually do.

Pete2