Do you think that it'd work to filter out enough of the junk to make the leftover fluid (mostly) harmless to the cave?
I think it would filter most of the biological material out of the fluid down to .2 mircons (that is what it is made to do) thus I would theorize (needs tested) that what would come out of the filtered end would be slightly acidic salt water. Which would be much safer to the cave than current practice.
Would you still store the liquid in a bucket or dump it on the ground?
You can dump it straight onto limestone (not gypsum). Since limestone is formed at the bottom of an ocean there will be trace amounts of salt in the cave anyway. The acid neutralized by the base element in the limestone, thus allowing it to be “safe” for the cave environment.
This idea should be tested first in a controlled environment and a non-iodide based filter should be employed. The filter needs to be chemical free for the idea to work.