It's a good suggestion. I would go a little further and offer this version of the entire paragraph that circumvents any mentioning of the 'claims':

"Although the empire had a multi-ethnic character during its history and preserved Romano-Hellenistic traditions, it became known to most of its western and northern contemporaries as the Empire of the Greeks due to the increasing predominance of the Greek element. The use of the term Empire of the Greeks (Latin: Imperium Graecorum) to refer to the Eastern Roman Empire also implied that in the West it was no longer seen as the Roman Empire. The authority of the Byzantine Emperor as successor of Roman Emperors, was challenged by the coronation of Charlemagne as Holy Roman Emperor by Pope Leo III in the year 800. Needing Charlemagne's support in his struggle against his enemies in Rome, Leo used the lack of a male occupant of the throne of the Eastern Roman Empire at the time to claim that it was vacant and that he could therefore crown a new Emperor himself. Whenever the Popes or the rulers of the West made use of the name Roman  to refer to the eastern Roman Emperors, they preferred the term Imperator Romaniæ instead of Imperator Romanorum, a title that Westerners maintained applied only to Charlemagne and his successors."

I'd leave the last sentence though since it demonstrates that there was still a certain ambiguity about how Popes and other western rules saw the Byzantine Empire.