"REMARKABLY, the Khazars, a people of Turkic origin, converted to the Jewish religion sometime in the 9th century, beginning with the royal house and spreading gradually among the general populace. Judaism is now known to have been more widespread among the Khazar inhabitants of the Khazar kingdom than was previously thought. In 1999, Russian archaeologists announced that they had successfully reconstructed a Khazarian vessel from the Don River region, revealing 4 inscriptions of the word "Israel" in Hebrew lettering. It is now the accepted opinion among most scholars in the field that the conversion of the khazars to Judaism was widespread, and not limited merely to the royal house and nobility. Ibn al-Faqih, in fact, wrote "All of the khazars are Jews." Christian of Stavelot wrote in 864 that "all of them profess the Jewish faith in its entirety."
I think the claim of the khazars to go back to their homeland is rightful, but then their homeland is Khazaria.
The khazars should pack their things and go back to central Asia, Palestine belongs to Semites, not to khazars.