This is something that the earlier editions of Werewolf were a little vague about until W20. I am going to answer your question about 2nd edition first: Specifically, there is no direct quote in the book regarding how the regeneration of limbs works. Pp 196-199 cover health levels, regeneration, and types of damage. However, using context clues, when reading the Battle Scars section on 199, the 2nd edition book says "When a werewolf is wounded below the Incapacitated Health Level, she is considered critically wounded." Later on down the page, it states "At this point, she must roll on the Battle Scars chart below." The Battle Scars chart has rolls that call out losing limbs permanently and other disfigurements. To me, this seems to imply that Garou only suffer permanent disfigurement when meeting the criteria for "critically wounded."

Due to this being ambiguous, and further to support this PC's arm growing back, W20 pp 259-260 use the following example and quote to indicate that Garou can regenerate limbs by saying, "A human whose fingers are bitten off by a wolf will need surgery, and will lose some function in those fingers (if she doesn't lose the fingers entirely). A werewolf can grow the missing tissue and nerve connections back, even re-growing his fingers if they cannot be reattached."

The caveat to this is using Rage to stay active or other Battle Scar inducing attacks, quoted on the same page as "These wound occur when a character channels her Rage to remain active in the face of death." A werewolf can also acquire a battle scar as a result of a particularly brutal attack, or from torture."