The FAQ at your link says that there is no problem with ocean disposal of the brine, which is only twice the concentration of normal seawater. If you dump that into the ocean, it will quickly be diluted and raise the salinity slightly. Got any evidence that the salinity increase will kill fish? If you filled a tank with the brine and dunked a fish in it, that might do it.
Sea grass and coral seems to be a bigger concern than fish, though some fish may be affected by salinity.
"Overall, it would appear that benthic infaunal communities and sea grasses are the most sensitive to the acute effects of concentrate discharge; some communities seem to be tolerant of effects of up to 10 psu increases, while others are affected by increases of only 2-3 psu. However, few studies have evaluated discharges to embayments, where less dispersion of the discharge may occur, and the chronic impacts on demersal vertebrates, particularly those which have significant life history behaviors (i.e., reproduction, migration) driven by salinity variations."
There are also many concerns with the effluent than just salinity.
