Distilled water is a better solvent than tap water because the driving force for the first few ions to jump into solution is the difference of the logarithms of the concentrations. A pure salt would have a concentration of 1 and the log of 1 is 0. Brackish water, say 1% saline, would have a concentration of 0.01 and the log of that is -2. The difference between 0 and -2 is 2. And more salt wouldn’t dissolve into that water very quickly.
But Sierra snow melt might be 1 ppm in salt. 0.000001 the log of which is -6. A difference of 6. And it would dissolve solutes more quickly than tap water does. “Corrosion” (actually dissolution) rates in metal pipes at Hetch Hetchy are high due to this effect.
And for distilled water, with concentrations below a ppb or pp-trillion, the difference would be 9 or 12 or higher.
So there is a theoretical basis for using distilled water to remove residual chemicals from a filter element.
Lacking distilled water, I’d consider flushing with dilute vinegar and then rinsing with tap water.