Taking someone else’s stuff using the rationalization “they shouldn’t have left it lying around” is stealing, yes. What if your daughter went to college and did this to a roommate?
Picking up things that are your child’s responsibility to keep in their place and telling the child that, as explained beforehand, the things are to be given to someone more deserving or that the child will have to earn the items back is something else again. That is imposing a natural consequence as a learning experience during the phase of life when the cost of the lesson is still low to the pupil.
If you don’t give the gift cards back, you have to tell the child what happened to them and you may not keep them for yourself. You could, however, put them into a family fund for gift-giving to other people, provided that this penalty was something the offender could have fairly predicted before the offense.
I agree with SMHW: If you leave your stuff lying around the same way, you should subject yourself to the same consequences, in order to teach by example and to establish an atomosphere of fairness. Adolescents have a very high sense of whether or not they are being held to a higher standard than people who are older and ought to be expected to behave just as well, especially the parents making the rules.
I think it is a very bad precedent for the “finder” to expect to automatically benefit from their “discovery”, let alone that they give themselves permission to pocket the whole “find” without trying to notify the person(s) they know is likely to be the owner. Rather, it would be better if “finds” go into a community fund that does not unduly reward the finder.
Children should be taught that ethical people make an effort to get lost items back to their rightful owners. That attitude makes for a far kinder world. Be honest and impose just the kind of “finder’s fee” that you would insist on giving to a stranger who made such a kind gesture to you. If you would give nothing, then think about that.