Is there any legal impediment to us going to a foreign sweatshop and giving out money?
It would not violate any US law. The country where the ‘sweatshop’ is located may or may not have laws on the subjects. Note: It would NOT be a GAP sweatshop. It would be a sweatshop owned by some company you will never hear of that sells products to GAP. I promise you, regardless of the control GAP may have, they DO NOT own the sweatshop.