Provide evidence of a new peace in the lands they travel to get home

From the text:

Before long the dwarves could be seen coming up the valley at a great pace. They halted between the river and the eastern spur; but a few held on their way, and crossing the river drew near the camp; and there they laid down their weapons and held up their hands in sign of peace.

In their day the last goblins were hunted from the Misty Mountains and a new peace
came over the edge of the Wild. It was spring, and a fair one with mild weathers and a bright sun, before Bilbo and Gandalf took their leave at last of Beorn, and though he longed for home, Bilbo left with regret, for the flowers of the gardens of Beorn were in springtime no less marvellous than in high summer.

Then the elves of the valley came out and greeted them and led them across the water to the house of Elrond. There a warm welcome was made them, and there were many eager ears that evening to hear the tale of their adventures.