You can pump brine water back but if I recall you can't just dump it all back at once because it's so highly concentrated. Ideally you would be able to find an alternate use for it.
In CEDI at least the ions are trapped in a resin then are driven across a membrane by a charge, on the other side of the membrane you run water to flush them out.
Some comment in the article left me thinking they end up trapping them in the media and have to reverse charge to release them so I assume it would operate pulsed and presumably have a valve to dump the output during regen.
Though I'm a little confused in that normally CEDI is used after RO because the CEDI media is pretty sensitive to fouling and also doesn't work well when the water conductivity is highly variable. Maybe they solve the fouling with charge reversal.
...who knows, because popular coverage of this stuff never hits on the important parts and almost never links the relevant publications. There are many ways to make drinkable water from seawater-- making them some useful mixture of energy efficient, cost effective, portable, waste-water efficient, and reliable is the actual hard part.
given the size of the thing it's likely to be positioned very close to the water source, so I expect it just dumps it outside the device. I mean, if I was running it on a boat, or next to the sea, I'd just basically pour the waste out right next to the device.
And I agree, at ounces per hour there's no need to dilute the brine, just dumping it is fine.
I thought the metal plates were collecting the salt but the article and video don’t make it clear.