You will find the Mic input actually puts out around 1-1.5V as power for the microphone, and shorts that to ground to signal that the pushbutton on the mic is pushed. You need to feed it via a non polarised capacitor of around 220n with a 10k or so value resistor on the phone side to ground, as this will tell it the mic is connected, and the signal will probably be under 100mV peak to peak at most. Often the socket is 4 way as well, with ground as the last position, and mic as the next, with right and left audio being the top ring and tip respectively. you might have to use a cable for the handset ( or a knockoff) and trace the wiring for the mic to feed it the signal.