To recover ownership by paying a sum is one of redemption’s definitions. Reconciliation is another way of saying this; to reestablish a close relationship with.

“And by the blood of Jesus, everything in heaven and earth is brought back to himself—back to its original intent, restored to innocence again! Even though you were once distant from him, living in the shadows of your evil thoughts and actions, he reconnected you back to himself. He released his supernatural peace to you through the sacrifice of his own body as the sin-payment on your behalf so that you would dwell in his presence.” (Col. 1:20-22, TPT)

As his restored children we then become representatives of the family. “Now then, we are ambassadors for Christ, as though God were pleading through us: we implore you on Christ’s behalf; be reconciled to God.” (2 Cor. 5:20, NKJV)