I used to foster for GAP (Their Seymour Location) and I was always impressed with their thoroughness as an organisation.
I wasn't a grey 'fan' before I fostered - but now I love them, they are a hoot! I fostered 2 cat-safe greys and one that wanted to eat everything that moved (in all honestly - to me they were no different to any other dog)
From my own personal experience - They are fun, loyal, keen to please, easy to train (you have to go through a series of dog "experiences" while they are in compulsory foster care - to expose them and report on their behaviour - so the system is thorough and can place dogs with the most suitable homes.
My only concern is that a lot of people who want to get rid of their greyhounds CLAIM that they have been through GAP - But they haven't - So unless GAP is your direct contact, I would get the current owner and dog information and contact GAP directly to confirm that she is indeed a GAP dog (as GAP dogs don't have to wear muzzles in public etc - so it's an important thing)
P.S. Buy an extra couch - they are 70km/h couch potatoes - They want 20 minutes of exercise and 3 hours of napping haha. You might not get your current seating back!
Asha - 22/05/15 Wolfhound cross a Dogue De Bordeaux X American Bulldog.