De-ionized water is fine for replenishing batteries.
Distilled water is also fine for the task.
Both styles have essentially had all (or most) of trace minerals and chemicals removed but through different processes.
The aim is to not add any minerals that would conflict with or neutralize the sulfuric acid in the electrolyte fluid.
A gallon jug of either will usually outlast many batteries before it is empty.

Use your wife's water that she uses for her steam iron and then you do not have to mess with a jug of water in your shed, or garage.

She should be using Deionized or distilled water, so the steam iron does not get gunked up.

Wife with an iron? What's that?

Wife?
What's that?

Man, I love this bar!

No wife? Who would cook and clean?

Old batchelors should do as i do: When all of the dishes get dirty, just open the window over the sink, and pitch them all out! Then go buy a ton of paper plates, and problems are solved. Plus--you can burn the plates in yer fire-place, or a wood-fired stove! Simple, huh? RJ

One thing i forgot to say:" There are those whose main ambition in life is to confuse the public, thereby making them buy stuff that is no better or newer than the old fashioned things we have relied on all these years!"
All that in the basic method of advertising myriad things, in many different shapes and forms, that do the same thing that they have done in the past. Like "Ionized" water. Probably $5 a gallon. Distilled water is around a buck a gallon. Haven't bought any lately. Of course you can buy distilled water at the grocery store for $1 or$4. Same stuff.
Like old P.T Barnum said----- by RJ

So the consensus is, I should throw away my battery and just get myself a wife! Now on top of the cooking and ironing duties, is she also supposed to cut the grass?

Yes to all that. And to be truly "green hearted", the mower should be a zero emissions push driven reel mower.
Well, maybe not completely zero emissions.......I expect she will emit some CO2, especially on the uphill grades.

Oh, Mownie! I'd guess if the Op would post pics so we would know if the advice was taken... We have a Lotto on this or somethin'?

Mownie--ya made my day! Rusty