In my extensive experience in Ancient (and not so ancient) history, every battle and siege seems to have a reference to “and they poisoned the wells so the enemy couldn’t drink.”
But how do you UNPOISON this font once the enemy has been gutted and sent home early? Especially the ancient times where I suppose it was harder to treat water. They had to have done something to fix the wells.
The history books never tell us the details . . .
You probably just wait a while for the poison to break down naturally or be diluted into harmlessness.
Dig another outside the contaminated soil.
It depends on what was used to poison the well. If they threw in the caracasses of dead animals, you’d just pull them back out and let nature take its course. You could also dig the well deeper, below the contaminated level and the fresh water would eventually refill the well.
You could also just dump the water into a settling pond and wait it out. Lastly, even the ancients had a pretty good handle on filtration.
You keep extracting poisoned water until the remaining poison is diluted to a safe level by inflowing water from the source.
you keep testing the water using prisoners until they stay alive in large numbers?