I don't agree with what is said on MN. We used pads and kept moving them nearer the door which worked. But she (my darling little doggie) was put in a kennel too, in the house and took out to do her business. It soon dawned on her that she had to do it outside.
Also, you should be giving the treat where you dog toilets, not when he comes back in. Go out with him and when he goes say "do a wee" or "do a poo" and then treat if he does. Mine now wees on command, especially when we are out or going out in the car but she does it when we are on the scooter too. Get words into his vocabulary, but stick to the same command for the same task. The main key is to keep on doing it, just like you would with a child.
downtoearth Does your greyhound have anything in her cage which smells of you or a toy which she cuddles? You may have to give her your dressing gown or nightdress, something with your scent on but which she can cuddle into. Again, try commanding her to wee, try making her associate the action with the word. Just keep repeating "wee" or "poo" if she does one when out and she will start to associate it. Treats and positive praise when she does it. Also there are vests on the market and they give your dog a hug, for separation anxiety issues. Thundershirt they are called, look them up.
Do your dogs do any other commands like fetch, sit, beg, come or lead? Maybe some puppy lessons would help? Or just spending oodles of time teaching over and over again. Patience and consistency is the key, I think. Especially a rescue dog, lots and lots of cuddles. They ultimately want to please you, so you have to teach them how to. Good luck. x