Wasn't the old Ethiopean civilization almost completely built by Georgian and Armenian missionaries? My father has a book about the Ethiopic language and script, since he's lived there, and I've been also told (by Armenians) that it were Armenians who've designed the script. I have to agree, comparing Ethiopic (script) to Armenian, there are similarities.
Ethiopic
Armenian
So, what are the modern Ethiopians really claiming? If anyone at all, the Georgians or Armenians should claim it.