Jeremiah says that God will be praised not only for leading the Israelites out of Egypt, but for leading their descendants out of Babylon, as well.
Therefore, the days are surely coming, says the Lord, when it shall no longer be said, "As the Lord lives who brought the people of Israel up out of the land of Egypt," but "As the Lord lives who brought the people of Israel up out of the land of the north and out of all the lands where he had driven them." For I will bring them back to their own land that I gave to their ancestors. (16:14-15)
So Jeremiah's looking back to the Exodus and finding the relevance for his own time period. The Hebrews in Egypt forgot their true identity, couldn't remember their own God until Moses reminded them. Jeremiah sees the forgetfulness of the Judeans and their worship of foreign gods as a parallel case. But in a way, exile will actually cure it: the experience of punishment will rekindle a feeling of devotion in them, and lead them back to the God of Israel.