That works until someone starts manipulating the market by redeeming their dollars for water, selling the water on the market, getting dollars again, redeeming for more water and continuously profiting from the endless cycle.

This is actually why the gold standard ended. Money and real world materials will fluctuate in value and are sold on different markets. Having money pegged to a real world material means someone can take advantage of a treasury by manipulating those markets. This was happening with the US dollar, then the Nixon shock happened and no more gold standard.

Why would people in the future use a currency system that's similar to one that we used in the past and stopped using because it was fundamentally flawed and vulnerable to manipulation? I suppose if it's set in a small community where there isn't anyone that would work out how to manipulate the currency it might work. But if there were bad actors, you'd expect a water based currency system to be manipulated same as the gold based system was before the Nixon shock.

And to follow up on my own comment, imagine this:

• Extracting water from the martian landscape would literally be seen as a source of wealth, and it gives people a strong incentive to extract as much water from the landscape as is reasonably doable, thus giving society a steady source of water, which drives society forward.
• Maybe, 1 martian dollar ($1) would represent 1 ton of water, and 1 cent (or "bit") would represent 1 kg of water, which means 1000 cents/bits = 1 dollar.
• So you might have paper money representing 5c (almost a gallon) or 50c (let's call it a barrel) for everyday use, so when you go to a market to buy some food, you might pay for it either by paper money or by literally handing over water bottles.
• The paper money would have to be handed out by banks that store the water or at least are able to hand it out if somebody wants to redeem their paper money.

"Bury your water, kids."