I would be seriously worried that there's damage you can't immediately see. If there are chips in the ring, it's possible there are micro stress fractures in other areas that aren't showing yet but which some heat cycling may turn up... like when you drop a glass on your counter and it doesn't shatter, but then you pull it from your dishwasher a few days later and it's got a big crack in it.
Also while the damage looks like it's towards the edge, keep in mind even if the gears are "perfectly set" dead center of the teeth the pinion will slide up and down the ring slightly as you lay into the gas or come off it. I wouldn't expect the pinion to move that far down the ring but it could happen, and if it sheds any additional material you're going to have a diff ready to grenade on you.
Maybe another way to put this... however much better you think Toyota gears are over Nitro or Yukon or other aftermarket ones, I believe a new $500 aftermarket gear set from Nitro is going to be stronger and more reliable than this used and now damaged Toyota gear set. If your package was insured file a FedEx claim and also contact the seller. Otherwise I think the FedEx limit is $100, which is worth claiming but probably not going to cover the full price you spent.