Hello Patrick,
Here is my best guess of the phenomenon you are observing:
The input pin to the MCU has an intrinsic diode connected between the pin (anode) and Vdd (cathode), and there is also a pullup between these two points. You are coupling the RF signal into the pin, and the diode is rectifying the RF signal, which produces a negative DC component that is filtered by stray and input capacitance. This is why you are observing a solid negative impulse.
There are two possibilities - decrease the shunt impedance to RF ground, or increase the series coupling impedance to the input pin, or some of both. Reducing the pullup value and providing a low inductance shunt capacitance at the pin should decrease the shunt impedance. To increase the coupling impedance, the best way would be to use shielded/coaxial cable to the switch, but other series inductance or resistance may help. The twisting of the wires might help to some degree because you are increasing the distributed shunt capacitance. You might also try an additional capacitor (say 100p) between the wires, at the switch end. But be aware that the connection of the oscilloscope probe may also affect the results obtained.
The ease of implementing a solution is likely to depend on the detail of you circuit board layout, and its grounding provisions.
I am not familiar with the details of GSM transmissions, but my presumption is that the phone produces RF bursts of 1 ms duration during ringing, and that these are at maximum power level. When the phone is subsequently answered, I assume that the power level is decreased under most circumstances.
I think that the input monitoring I previously suggested was also quite similar to Rocco's suggestion. However, I would probably suggest to test for an unbroken switch closure over a period of at least 100ms. If you were sampling at 1ms intervals, you would expect to see 100 sequential samples with low state, before a switch event would be registered. If any sample was high state, the count would be restarted.
Regards,
Mac