A TDS meter does not measure much change between unfiltered water and water filtered with a Berkey. This is normal and the answer has to do with what a TDS meter actually measures. According to tdsmeter.com "Total Dissolved Solids (TDS) the total amount of mobile charged ions, including minerals, salts or metals dissolved in a given volume of water, expressed in units of mg per unit volume of water (mg/L ), also known as parts per million (ppm). TDS is directly related to the purity of water and the quality of water treatment systems and affects everything that consumes, lives in or uses water, organic or inorganic, for good or ill."
This statement is both correct and incorrect. It is correct in what a TDS measurement consists of, which is the "total amount of mobile charged ions, including minerals, salts or metals dissolved in a given volume of water". It is incorrect in its conclusion that TDS is related to water purity and the quality of the water treatment system. If the measure of a water purification system was how close it could bring water to pure H2O, it might be correct. But humans need minerals to live. So useful minerals in your water are actually a good thing. A high-quality water purification system should filter out things that are harmful to your body, but leave behind the useful things like minerals. Black Berkey filter elements are designed to leave healthy and beneficial minerals in the water and extract unwanted heavy metals like lead and mercury, as well as sedimentary minerals like iron oxide and aluminium.
So if you use a TDS meter, you will find that the reading both before and after the water has passed through the Black Berkey filter elements is about the same. And so it is true. The Black Berkey filter elements retain all the beneficial minerals. So, of the things a TDS meter will actually detect, the Black Berkey filter elements will only remove unwanted heavy metals like lead and mercury, as well as sedimentary minerals like iron oxide and aluminium. Therefore, unless you have a significant amount of heavy metals or sedimentary minerals in your water, the TDS value will not change much.
A TDS meter does not measure the amount of biological and chemical contaminants (including e.g. chemicals, drugs, hormones, many pesticides and their residues, bacteria and viruses). Most importantly, don't rely solely on a TDS meter to measure whether your water is good. You can have water with low TDS that contains harmful bacteria. You can have water with a high TDS level that is perfectly safe (e.g. - pure, uncontaminated sea salt water ... although you wouldn't drink it, but that's only because it's mineral salt). So make sure you know what a TDS meter actually measures.