Does your system use salt?

Yes. To truly soften water and remove the hardness from it, you have to use salt. You can use a salt-free system, also called a water conditioner, which do not use salt but they will not reduce hardness in your water. They also will not treat iron. Those systems can prevent hardness from adhering to your pipes, but once exposed to air the water is the same hardness that it was going into the pipe.