OP, you are very right to be concerned. There are serious welfare concerns associated with greyhound racing. Not all tracks come under the GBGB mantle, and on these flapping tracks conditions are even worse - dogs run with no vets in attendance for instance. Course design and maintenance is often poor and leads to severe injuries while racing. Unless the dog is a top end one, these are rarely economically worth treating so dog is killed.
The greyhound racing industry simply cannot account for the huge gap in the number of grey pups that are born each year and the number that leave racing. Supposedly, racing owners are meant to find good homes for their dogs either through the RGT or via other charities - sadly, many don't. Take a look at the Tia Wall of Shame here - this is just one rescue that is logging the registered hounds - there are thousands of dogs like this up and down the country. I volunteer for a couple of greyhound charities - all our own dogs are ex racers and they have had a pretty rough ride. I also see the state many of these dogs are in when they are dumped or abandoned (have fostered and transported many).
In fairness I will say that I have met a small number of caring, responsible racing owners but sadly after many years of volunteering I must say that the price these dogs pay is too high for you to have "fun" with your colleagues.
I won't write an essay, but please do not hesitate to ask if you want any more information or for links to more websites etc.
And on a happy note, all of our dogs are now very much enjoying their retirement, and I'm delighted to say that the number of greyhound tracks in the UK is steadily reducing.