No, don't try to remove calcium. It can be done, but it's a pain and not necessary in your case.

Just be careful about dumping soda ash / baking soda into the pool. If you stay away from the pool store, and listen to us, that shouldn't be an issue. But pool stores -- especially BioGuard stores with the "Alex" computerized dosing monster -- seem to love to recommend simultaneous large doses of calcium chloride and sodium carbonate.