As the nation’s banks and financial firms emerge from the wreckage of the financial crisis, they are working out how best to lend to people with tarnished credit. Overall, credit-card issuers sent 418 million pitches to U.S. subprime borrowers in the first nine months of this year, double the year-earlier volume of 207 million, according to research firm Synovate, a unit of Ipsos. Despite the surge, direct-mail solicitations remain far below pre-crisis levels. (Synovate doesn’t track balance-transfer offers.)...