It should come as no surprise that grocery-store discount cards are just a gimmick, as The Discount Grocery Cards That Don’t Save You Money points out:
The bottom line: Sale prices — which were once available to all shoppers — are now mostly restricted to card holders in stores with cards and are called “card specials.” In our experience, items not covered by card discounts tended to be more expensive than at nearby noncard stores. As a result, we paid more at card stores than at noncard stores.