Before going any further, I would try to find out how the water got into the gray-water tank. My hope would be that an open faucet overfilled the gray-water tank. Also, if the shower faucet cracked from freezing, defect or over tightening it could allow water to flow down the shower wall and fill the tank through the shower drain even with the faucet turned off.
To fill the gray water tank, water has to be flowing down one of the drains leading to that gray-water tank. I would empty the tank and look for the problem before taking out the filter.
2015 Wildcat 282 RKX
2011 F350 Lariat, 6.7 L. Diesel, 8 ft., SRW, Reese R20