Alright, I know it's very unlikely, but still let's try to know more...
Every backing vocalist is credited on the album, except the one for the title track.
Now I have my theory: when they were working on the album at Steve's house Gillian was there at the moment of doing the backing vocals for the title track and she sang (the voice really sounds like her).
Those vocals were so good they decided to keep it on the following recordings.
They also decided not to credit her because it would have been like crediting someone who is not part of the band and, somehow, Gillian is not a true active member of New Order, but she never really left the band, you can't count her as a session vocalist... she's still a New Order member, maybe the new fifth member...
Please anyone with contacts with the band or management, or anyone meeting them at gigs ask about this, because I'll be probably wrong (maybe she's someone else and they just forgot the credits), but I'd like to know anyway...