Couple of thoughts....
Since this line is segregated from the rest of the coach and it has it's own filter, it makes me wonder if the filter itself might be coming apart and need to be replaced (defective) or if there is something else caught in the line and causing bits and pieces to come out over time. If it's calcium, you should be able to press it between your finger and thumb and it would crumble and fall apart in your hand and you should be seeing it throughout the rest of the coach unless you have filter differences (one that is a stronger filter then the other).
Has anything like this occurred before through the coach or anything you can think of that applied only to that water line? Such as any work that was recently completed to this line or toilet.... I don't have the answer yet, but thought at least I could help you brainstorm this one.
Where we've been:
2000 Rockwood Roo M-18 Hybrid
2006 Dodge Ram 2500 Auto 5.9 Diesel
Gone but not forgotten -1986 Rockwood 1003 PUP