The way that these programs work, it is no questions asked (intended to get even criminals to turn in firearms, to prevent them from using in future crimes/suicides). So a "show ID to turn in" policy is a non-starter.
Shameless promotion, but even absent such gaming I am quite skeptical these are cost-effective, https://andrewpwheeler.com/2022/08/21/gun-buy-back-programs-....
Making it so they only take working handguns, and if the gift cards were more on the order of $25-$50 makes it a more palatable to me from a cost-benefit perspective. But still evidence they actually work is pretty slim.