why shouldn't a subbie do work for whoever he wants, you employ a subbie to do work for a customer cause you cant do it yourself, i assume you make money from the arrangement, so if the subbie leaves a card for future work are you saying it is wrong, and if the customer wants more work done they contact you and you contact the subbie and you add something to the job, so basically you want to have control of who gets work done and want to make a profit from it, i think that is wrong. i appreciate the first company has advertising etc and a lot of people are proud of the fact they get repeat work, but in effect you want to stop your subbie doing the same.
say a customer contacts you to get more brickwork done as they were happy with the first work by your subbie, however the subbie isnt available and you get someone else who isnt as good, you get a cut so you are happy but the customer has paid more for a poorer job, but if the customer had the first subbie's number they would get the guy they wanted