Mitochondrial DNA is a powerful tool, admittedly. Yet, we have the Celts moving west, not east. I don’t see the support of the statement that the Germans were influenced genetically by the Celts moving back east.
Later agriculturalists from the Middle East began moving into Europe from the Mediterranean coast.
Obviously populations mixed ~ to a degree ~ but Northern and Western European populations came from those two refugia. Their Indo-European languages arrived THOUSANDS of years later.
For all practical purposes the Celtic and Germanic people are IDENTICAL but there are threads of mtDNA within each population that suggest various admixtures from outside.
In short, everybody in Europe spread out from a location on the Bay of Biscay or on the Adriatic until otherwise demonstrated. The flow has been mostly from the West to the East, or to the North, or to the South.
The very first population to "break out" of the Western refugia as the ice began to melt headed straight for the Arctic, as well as to North Africa, East Asia and to America. Later populations left the refugia as forests returned ~ but they, too, moved rapidly into Eastern Europe.