The parasite is introduced by drinking infected water, but the water is infected when the worm begins to emerge from the body and people immerse the open sore in the water to relieve the pain, allowing the worm to release larvae back into the water supply.
I'm no epidemiologist by any stretch, but my understanding of the rationale is that if all human infections are eliminated and re-infection prevented—i.e. no one drinks unfiltered water or exposes the water supply to guinea worm larvae—then the guinea worm's life cycle will be broken and the disease eradicated. There's no known case of guinea worm infection recurring after it has been eliminated from an area in which it was endemic, and this particular species doesn't infect other animals that could pass it on to people.
Whether that means the parasite is still in the wild and infection could theoretically flare up again because someone drink some unfiltered water, I couldn't say for sure. I suspect not, if "eradicated" actually means what it means.
That is assuming the larvae don’t infect other animals.