If the GC is or has any level of professionalism, he will instruct the subs that there is to be no smoking from here on out inside the home. The problem is that the GC is most likely not on the site all day long and there for it falls to the subs to police their workers.......

Do you have a contract with the GC? Did you spell out in the contract that once the house was closed up that there was to be no smoking in the house? Was there a penalty in the contract for breaking this clause in the contract? If you answer no to all these questions, then you're at the point of almost no recourse other than asking again and again that no smoking be done in the house.

You might try asking the subs themselves and explaining your concerns for your health reasons and that you don't appreciate the smell of smoke in your home.........

Good luck.

I make it very clear on job sites that there is no smoking permitted inside. Ever ... at any stage.

However, there are many new subs coming and going during a construction project so just put up a paper sign where workers enter the home that says " At homeowners request no smoking is permitted at all inside the house"

I don't care whether it's in your contract or not. Common decency dictates that you don't smoke inside anyone's home without their permission. End of discussion. Full Stop. A guest in your home would not do so, and certainly someone who is working for you should not do so. I would talk directly to the supervisor, and if he's not there talk to the offender. If spoken to respectfully they should appreciate that this is your home and abide by your wishes. Putting up a sign is also a good idea for a constant reminder (esp. for workers new to the site), but don't be too passive, this is your home that happens to be where they work, not vice versa. That said, I just sent myself an email to make sure we insert a "no smoking" clause in our builder's contract--thanks Mr. Kutch.

I too don't think this needs to be a contractual issue. It's a matter of common sense, decency and respect. I would imagine that simply asking nicely would do the trick. Whomever is there (be it GC crew or subs), is there to do a job. It should be a simple matter of bringing to their attention your feelings about this and that should be the end of this.
A call/email to your GC repeating same is also a good idea.
Good luck!