Could further oil drilling remove an insulation layer of the Earth cores heat?
I think your basic assumption is incorrect. Removing oil and the 80 to 90% water associated with it would reduce the thermal conductivity of the rock formations. It removes these liquids which aid thermal conductivity across the myriad of very tiny pores that contained the liquids. In the US regulations have the affect of the water being pumped back into the ground , not necessarily into the same formation. Outside the US that is not generally the case. Without doing any arithmetic, this appears to be a minuscule affect on earth temperature.....Thinking about it a little , you could likely make a better case on the basis  of the heat in the produced fluids ( water ,oil, gas): I know difficult wells go into formations that are 400 F+ , overall average the average temperature of production is likely between 200 and 300 F. No doubt SPE has real data but I am no longer a member.