I'll try to help a little. I have the Sizzix pillowbox die and use it a lot. However, I hardly ever buy gift cards, so had to get an assembled pillowbox out and measure it.
I'm assuming a gift card is the same size as a credit card, 2-1/8". The width of the pillowbox when it is assembled/glued together is 2-1/8". But when you "puff" it up, you can't really get the card to go into it. It is the same size as the card, but there is not enough "give" to get the card in. Kind of like putting cards in envelopes, you need a little extra room over the actual dimension of the card.
That said, I love the die and use it for all holidays, and put mini-Hershey bars in it. Two of them fit very nicely. I just got through making a bunch with Halloween paper, then used my 2" scalloped punch and put cute Halloween stickers in the middle.
Here is a sample of the scallop/sticker routine, only it's on a wrapper, not a pillow box. I made these for Valentines. The same concept works great on the pillow box and is easy and quick to do.
Valentine Candy Wrappers - Hello Kitty by buggainok - Cards and Paper Crafts at Splitcoaststampers
pillow box dies
