No, not for online Cash Back. Online purchases are tracked through affiliate links when you click through from Price.com or the browser extension, so no card details are involved. Online Cash Back works no matter which card you pay with.
Card linking is only needed for in-store offers, where the merchant needs a way to recognize your purchase at the register. Enrollment runs through Olive, a PCI-compliant card-linking provider that works directly with Visa and Mastercard. American Express is not supported.
Enrolling takes seconds, needs no banking login, and your card number is never stored on Price.com servers. You can use Price.com for online Cash Back, coupons, and price comparison without ever linking a card.