Calcium usually deposits as a white crust on the side of the tank at the water line, but I suppose it could flake off if there's a lot - and with hard water there could be a lot.
If they sink, you'll hoover them up when you do a water change. For those on the surface you could try the method used for oily films. Turn the filter off and when the water stops moving lay a paper towel flat on the surface. Then lift one side slightly and draw the towel across the water surface to the side of the tank before carefully lifting it out of the tank. If that helps, repeat till most of it has been removed.
Then turn the filter back on.
Do you have filter wool/floss in the filter? That should trap any bits that get sucked up.