Often times, when stores run promotions like this, they have to have proper documentation in order to support giving out the giftcards. The easiest way is to have you give them the coupon, they would then reconcile it at the end of the shift. This would be a way to ensure that employees are not stealing giftcards. While they could have explained it better to you, you are unfortunately not being very reasonable when you expect them to make an exception when you lose the coupon. I feel for you, but you shouldn't have lost the coupon. They are under no obligation to give you the free gift card without it.