DTMF isn't transmitted in secret. Of course they could eavesdrop on what you entered through a keypad. Keying it into a machine listening to an unsecured phone

DTMF isn't transmitted in secret. Of course they could eavesdrop on what you entered through a keypad. Keying it into a machine listening to an unsecured phone line is the equivalent of sending it in plaintext and just as vulnerable as telling it to an agent on the other end of the call.