Sorry, Diana, if the card can be exchanged for the item without any money leaving my pocket that constitutes "free" to me.
Say Una's item costs $160. Assuming the card is worth $160, using the card means she pays nothing. If she buys the item at Site B, after the discount, the item costs her $80. Granted, she still has the possibility of finding something else in the future at Amazon, but there is nothing to guarantee that a future purchase would give her as much pleasure as knowing that she has the item she wants without any money leaving her pocket.
But, as I said, I've always been a bit dubious of the logic that seems to imply that spending more money now will guarantee I'll come out ahead at some future date. Sometimes it works out just fine, but life has a funny way of throwing curveballs at us, despite our best plans and intentions. I'm sticking with my vote for using the card now.