If you earn forgiveness, God will forgive. That leads us to the second word, vindication. When God returns them to their home, he sets forth some new promises. He says they will be called by a new name and be a glorious crown in the hand of the Lord. God also says that all the nations and kingdoms will recognize them and their glory and they will no longer be called forsaken, or their land desolate.
Vindication means to support or maintain as a right or claim.
Because the Hebrews see that God has not abandoned them or forgotten them, they have greater faith in God. Because they realize God is with them always and will never leave them, and that they have been returned to their homes they rejoice. That brings us to our next word, rejoice. When they were returned from exile they realized all their faith that God would rescue them paid off and had basis for the faith to exist upon. Rejoice is a key word in this passage because it kind of describes how the Hebrews felt and acted when they were returned.