I'm wondering if there's an expression for those cards (not necessarily a bank card), that some companies use to promote customers' fidelity, by giving out promotions, etc?
I was thinking of using the expression fidelity card. Is it okay?
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Those are usually called 'loyalty cards', and they're part of a 'loyalty program'.
While loyalty card (as suggested by Glorfindel) is probably the correct generic term, the companies themselves often call them club cards, as if having one makes you a member of some exclusive club.