Me, I would be washing it. Unless you get the actual tar and smoke out of the fabric, it will not be clean. Press the top before quilting and I am sure it will look as good as new.
Sun and fresh air may get the smell out, but the fabric will not be clean.
I had to clean a cabin that had had smokers living in it over the winter. It had already been 'cleaned', by some one who covered up the smell. They had aired out the curtains, lightly cleaned the walls etc.
I washed those curtains in the bath tub and you would be amazed at how brown the water turned as the smoke was washed out.
Cattailsquilts mentioned lambskin. I have washed those too in the washer and dryer. I also wash wool mattress pads at least once a year in the machine, hang those to dry if I can, otherwise they go into the dryer.