The medallion and the jade pieces stay with Breach. As far as Breach is concerned, he is the only one still in pursuit of the Cultist and those items are the only link we have to it right now. Disputes will be settled via Tyrogatore's rules of ownership.
If we are splitting up, Breach will divvy up the gold he recovered from the temple floor inlay into approximately equal chunks to distribute to the group that confronted the Blue Beast.