Soaking it in salt water is the recharging I was taking about above. Salt water is largely sodium ions, so the pillow will release magnesium and calcium ions and then take up sodium when in the salt water -- a sodium rich environment. Then, when you place it in your hard water, there will be more calcium and magnesium than sodium, and the exchange will happen the other way.
Again, I think that it is a question of scale. I doubt that a very large difference can be made. It will be very impractical for a large tank. And considering you should be doing regular water changes, you will be constantly putting more magnesium and calcium back in anyway.
I think that the best idea is to go with fish that will be fine with harder water. There are plenty out there, and the vast majority will be fine in harder water.