It was entirely an accident. Likely that Extraterrestrial was trying to keep an eye on Kit & Grace, to make sure they didn't escape and thus that they could still be under observation. Then it was hiding or got lost in the Briarcliff corridors, waiting for Kit, Grace and Lana, and ran into Jude by accident. Perhaps it also used some sort of scanning equipment to tell that she was intoxicated and thus not a danger.
Alternatively, she might have been an earlier candidate in their breeding programme that they abandoned once they discovered she was infertile.