Believe me your retriever would know she is in season, no matter how 'clean' she is.
Why do they specifically want a girl?
And puppies, in partic. Lab's, are as much work as a new born, and then some! Lab's chew everything, including people, clothes, shoes, all the normal stuff, plus curtains, window sills, kitchens, walls, doors, skirting.
Obviously, there are good sides as well, but I would think very carefully about introducing a bitch, it not only would be bloody hard work to keep them seperate while she is in season, but it really wouldn't be fair on you GR, and if they did manage to get to each other, you would be responsible for the puppies.