Connecting Electret Mic to MT8870 Decoder Module
I plan to power the mic at GND and VCC pins and connect the AUD signal
  to the right and left channel of one of the jack plugs on the stereo
  cable.


First things first; it's not a stereo input; it's a differential input that the MT8870 uses but, it can be wired single ended.

I'd interface like this: -



The attenuator inside the red square is something I've added that you can easily make (and adjust). The two resistors could be a potentiometer (circa 10 kohm) and the capacitor will be fine with a value 100 nF for DTMF signal frequencies.