Oscilloscope Probe - How to measure a sensitive circuit
Try normal 10MOhm 10:1 probes first. 

There's still plenty of caveats such as collecting disturbing signals due ground loops, interfering fields and potential difference between your circuit GND and oscilloscope's GND. Impossible to guess all without seeing. You may need 2 channel measurement in difference mode to compensate some disturbances.

Your best bet is to get a local advanced oscilloscope user to help. 

ADD due comments: The problem seemingly is that inserting any long wires in parallel with the piezo part, the pulses get distorted in an unknown way and the operation stops.

A suggestion: In place of your "opamp", which should be a speedy comparator with sturdy enough input for your voltages, you surely can put a voltage follower amplifier. It's output can be measured without affecting the pulses. I guess wires make a resonant circuit which creates some ringing at several megaherzes. You can see it as "no function" if there really is an opamp instead of a proper comparator.