According to wikipedia the right ascension and declination of the Milky Way Center and GJ 1214 b are:
MW 266.4168333 -29.007805560
GJ 1214 b 258.828925 4.963802778
(Expressed in degrees), giving them an angular separtion of 34.75 degrees, fairly well separated. Wikipedia also gives the distance from the sun to GJ 1214 b as 42 light years. I think it’s safe to conclude the story is weakly written.
Okay, that rules out option B. I'm pulling for option C, because I don't really want a massive black hole 40 Light years from earth and heading our direction.