A number of personal items were also stolen in the burglary, which happened when a rear door was forced at an address in Red Beck Vale on 15 July.
Enquiries have revealed that the bank cards were used later that day to make purchases in Bradford and Shipley.
Detective Constable Simon Turton, of Bradford District CID, said:
“We would like to hear from anyone who recognises these men, or anyone who may have seen them in the Shipley area on that day.
“Information can also be passed anonymously to the independent charity Crimestoppers on 0800 555111.