Bear in mind that 3x5 cards are typically the tool of the freebie through the mail collector. And Mantle rarely, if ever, responded through the mail.
And when he was doing card shows charging high rates (for the time), what are the odds someone was going to pay the high fee for a signed index card? Almost nil.
In person is always a possibility, of course. But if you were playing the odds, the fact that it is on a 3x5 card in and of itself, tells you authenticity is unlikely.