Op-amp circuit works correctly only when the oscilloscope's probe is connected to it
Connect a high value resistor from pin 3 = op-amp non-inverting input (OA+) to ground. 10 megohm may be OK but 1M better and lower still better still - but lower will load MK1 more. 

What is [very probably] happening is that there is no DC bias to the OA+ input and in the absence of signal the very high impedance input is driven by a combination of inset-offset  voltage, input bias current and the prior positive input  - all stored in or charging or discharging the capacitance at OA+ to ground. 

Oscilloscope probes and fingers (when connected to bodies) tend to make such arrangements work better or differently by providing a small amount of "ground reference" current or a degree of sink impedance.