Yes, I know water should be above the water line. I was given the impression that the 4 bags of salt would last 6 months, which I thought was a lot. I will add salt. Thanks.
The calcite neutralizer runs every 3 days.
I would try to see if the calcite has bed expansion. You can see this if you have a natural-color (unpainted) tank, and shining a bright light through, looking for the shadow. I think 3 days is shorter period than usual for calcite. But the backwash should be vigorous enough to expand the media.
So how is this relevant to your crud in the brine tank? Maybe not at all, but I was thinking that one possiblity is the crud is coming from the well, and the calcite has generated channels big enough to pass the crud. Good backwashing should get rid of channels. Regardless of possible or impossible relation to crud, you want good backwashing maybe once per week. I am not a pro.
More likely the crud is due to impurities in the salt.
Another possibility is that somebody used your brine tank as a waste basket at some point.
I would skim out the crud I could. Then I would add salt so that some salt is always above the water. If you are short of salt, pour the salt to one side so that some salt peeks above the water.