If you are a Shop Your Way reward member with Sears and Kmart you can link a Visa card to use with their Reward Partners to receive points with Sears and Kmart.
As an added bonus for linking a qualifying Visa card, you will receive 7,000 points ($7.00). No where does it mention that you need to make a purchase with Sears, Kmart, or one of their reward partners to receive the free points.
Some fine print of note:
** Offer good through 3/31/2014. Offer limited to 7,000 points per member. Not available to members who have previously registered an eligible Visa card in the program. Members can register up to three eligible Visa cards. Points will only be awarded for the first eligible Visa card registered by a member. Points will expire 14 days from receipt of email notification that the points have been awarded.
Also, if you actually do want to earn points for making purchases with one of Sears and Kmart's reward partners, you need to make sure not to enter a PIN number when making your purchase. Fine print on that:
†Not all transactions made with your registered card (including PIN-based transactions, payment through a third-party digital wallet or payment app) can be monitored for eligibility to earn points. Do not use a PIN when making purchases if you want the transaction to be applied towards your offer completion.