No need to panic. I also use a Zerowater filter. I'd be worried about drinking distilled water after exercising or in high heat because it can lead to hyponatremia -- low blood sodium levels (see https://en.wikipedia.org/wiki/Exercise-associated_hyponatrem...). Because your body is sweating, you're losing a lot of salt that your body needs. Drinking distilled water will pull even more solute out of those cells as the solute chases water (i.e. the cells are hypertonic) until its in steady state, but of course it needs to replenish what has been

However, during normal daily activity and by eating, you're supplementing your body with enough salt (and other solutes) to compensate for what isn't in your distilled water.

Now it's a totally different question whether we're getting PFAs out of our water with the Zerowater filters. That should rightfully incite some panic.