Hi Rachel
As Dawn says this is a very sensitive subject and could well be a very great shock to the lady concerned as she will think the people who brought her up were her parents. I can't tell from what you've said earlier whether your nan knows about your findings, or whether you've even discussed it with your mother or father - you don't say which nan you are talking about.
If your nan and this lady really are twins, I'm sure they would like to know about each other, most twins do.
Take care
Lizzie
ps. It is always possible, I suppose as the travel documents show guardian that the person who was "adopted" does know about her twin and is just waiting to be contacted.