I was curious so I checked the terms of the gas program (also at Giant Foods... same as Dave) and it looks like they EXCLUDE gift cards from accumulating points.
There are no Kroger stores around here
Terms and conditions
Fuel savings are limited to 30 gallons of fuel per vehicle per purchase, or limits placed on your payment card by your financial institution, which may be lower. Total discount cannot exceed price per gallon. Offer available at GIANT stations. GIANT Rewards points earned at participating GIANT locations only. Only purchases made with your BONUSCARD are eligible. Net purchase excludes milk and cream (PA & VA only), alcohol, tobacco, money orders, postage stamps, lottery tickets, gasoline and other fuel, <span style="color: #FF0000">gift cards</span>, amusement park and any other tickets, Western Union wire transfer services, fax service, copying machine service, coin operated vending machines, utility payments, prepaid telephone calling cards, prepaid wireless, delivery charges, dry cleaning, fund raising activities and donations, returned check service fees, payments toward store charge account balances, personal shopper fee, bottle deposits, and prescriptions (prescription copay amounts, except those for state and federally funded prescription plans including Medicare, Medicaid and government funded programs, will earn Extra Rewards points). Gas Rewards points expire on the last day of the promotional period. All Gas Rewards points available at the time of a gasoline transaction will be redeemed. Visit your participating GIANT stores for program details. Offer may be modified or discontinued at any time without notice. Not valid where prohibited by law.