Extraterrestrials is one word. Extra terrestrials suggests you have a surplus of Earthlings (free to a good home!), but it says nothing about people from other planets.
Y’know how it’s correct to capitalize the name of your own home planet (assuming you are from Earth)? Well, it’s also correct to capitalize nouns or adjectives formed from that name. Thus, always capitalize Earthling (although it’s s stupid word — Terran or even Earther is much better).
There seems to be a dropped word — or perhaps just a misused word — in the latter part of the example sentence, but I’m not sure what was intended.
Earth is visited by extraterrestrials who claim they’re refugee Earthlings from a past extinction [event?], returning to their home planet.