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It depends on exactly what the store is doing.
If the store is representing the extra charge as a donation to a specific charity, generally, the customer can deduct that.
If it’s far more vague, like, “Give $10 to help poor kids in Africa” the ultimate destination for the funds could be the company’s own ledgers, which it would then use for its own charitable activities and collect the tax deduction, as long as they “help poor kids in Africa.”
And some stores are just lying. CVS, for instance, was sued as part of a class action suit when, after the company pledges $10 million to the American Diabetes Association, then collected money from customers to fund that pledge.