Dehairing water is hot, but not end-all-life hot, thus, once used it is inadvisable to reuse it.
Dehairing is a process used in meat processing while the carcass is still intact, the goal being to decrease the amount of surface that possible disease vectors are present on.
The needed temperature of the water is 60C, a few minutes of immersion in that water will loosen the follicles. Higher temperatures lead to less effective dehairing, although near-boiling water would be preferable because that would be good against bacteria in the water, which are possibly transferred to later-scalded carcasses in 60C water. There is a technologically more challenging technique using steam condensing on the carcass (the challenge being regulating the steam temperature so the condensate on the skin has the right temperature) that avoids dipping several carcasses in the same water. Contamination of the meat from without is the largest contamination source (alternative being bacteria already present in the meat).
Here is one possible root of the belief that reheating the water is somehow not as good as 'freshly' heating the water (ignoring that it is impossible to not reheat water on earth, as all water boiled at least once throughout the Hadean): Reheating water that has already been used as scalding water means reheating to unsafe temperatures a soup of hair, blood and feces that had already not been safe from the inception.
There is no indication that reheating waters has any effect on the efficiency of that water in dehairing. Recycling water is only discussed in the context of hygiene.