Here is the best way to make sure you are given your Gift Card, and I included a plan B just in case:
First thing in the morning, call the store number. It will automatically connect you with support, so tell them you need to be connected directly to the Senior Customer Specialist on duty at the store because you did store pick up and still have not received your EGC (electronic gift card). When the SCS talks with you they should hopefully know why you are calling if the support agent explained the reason for the call. They can assist you quickly if you give them the Web order number from your pick up (should begin with a W on your receipt). They should be able to get you resolved then.
PLAN B: If the support person has a hard time getting an answer from the store (which can happen once the store gets busy) tell them to connect you with someone in Post Sales, who should ALSO have been told the reason you called, and with the same Web order number on your receipt, they will be able to get you set up with the gift card by email. Hopefully this helps you to get your gift card quickly and hassle free!