Based on the picture, asking for a new transfer case won't fix your problem of a leaking rear differential. Asking for a new rear axle assembly would, but the transfer case is at the OTHER END of the driveshaft.
ok...anyway, a small amount of fluid can look like a lot when spread out like that. I'd ask the service manager to see how much actually leaked out - if it wasn't much you are fine. But if it's mostly gone and was on the verge of failure due to low oil, might be worth fighting over, or at least asking for an extended (100k) mile warranty on that part.