I had calcium scale and was able to reduce and finally eliminate over a period of time. It isn't a quick fix, and I don't know if it will work for removing the stains. I had no stains, just a layer of calcium scale.
When using PoolMath, after you have put in all your numbers you will notice a field at the bottom of the chart labeled CSI (calcite saturation index). This number should always be between -0.6 and +0.6, with a normal goal as close to zero as possible. Any further on the positive side causes calcium to come out of suspension and be deposited of surfaces as scale. Any further on the negative side and the water becomes corrosive, dissolving calcium, and can even dissolve it right out of your plaster or concrete. The trick, if you currently have scale, is to keep the CSI always on the negative side, but not let if get below that -0.6 limit. There are several factors that combine to produce the CSI, (temp, TA, CH) but the one you have the most control of is the pH. If you carefully monitor and control the CSI, always staying between -0.6 and 0, over time it will remove scale from the pool without damage. But, it takes a lot of time and patience.