I think that would be difficult to make happen. Earth movements associated with fluid or gas withdrawal tend to be very small and occur incrementally over time.
Tsunamis are caused mostly by earthquakes. Submarine landslides and cosmic body impact can also create tsunami. These disturbances can displace a large water mass from its equilibrium position which can create tsunami. Oil and gasexploration and exploitation can not trigger this mechanism.
The extraction of gas/oil can leave a void (like a cave). The overlying pressure can cause a collapse (like a sinkhole) under the ocean and this will generate a tsunami. Nothing can stop this process from happening.
Consider that opinions denying such a process can be synthesized by the oil/gas industry themselves and institutions sponsored by them. I once wanted to investigate hydroelectric reservoirs and possible earthquake/tsunamis generated by the water load over unstable landscapes. The industry contacted the head of the university who gave the order to "shut him up", meaning that I was not going to investigate it further. Apparently, that industry was giving a big donation to the university and did not want the investigation to find the cause of the earthquakes.