GRO certs are usually hand-written copies of the copy sent them from the RO, so won't help with the signature which will be only on the original cert (which hopefully your aunt has!).
If you are buying another one, I suggest getting one from the RO, and ask them for a photocopy of the original (which would be the one with the crossing-out).
One thing which has been bothering me is the parents recording their "adopted" child under her original surname. I've never seen that before. Quite often the original surname was kept as a middle name, especially when the child was old enough to remember her previous name, but this looks more like a foster child, especially if money was provided. That would also make more sense with the advertising. It would be very interesting to find that ad. and see who the contact was.
Sue