I'm a little confused by what the Engineer is saying. Here's my take on how bonding/grounding works and maybe I'm totally wrong ... The water, pool, other electrical equipment, ground around pool and pump are tied together and goes to the pump bonding lug making them all equipotential around the pool. The bonding lug on the pump should be attached to metal on the pump which in turn is connected to the grounding wire of the pump (or it is directly connected to the grounding wire of the pump which is attached to metal). The pump is connected to the outlet with 3 wires - Hot, Neutral & Ground in a plug and there is a ground going to the main panel - you are theoretically grounding the pump and anything attached to that bonding wire to the house ground. Maybe the wire from the pump to the circuit breaker isn't #8 bare copper wire but it also isn't a single little strand of copper either. 15 or 20 amp wire should be thick enough for low voltage grounding.
When the electrician took the ground off the pump and the sensation stopped it was because the circuit wasn't completed by you touching the water and it going to ground. Is it possible that you have stray voltage floating around - yes. Is the ground to neutral in your house compromised - maybe. Unfortunately the only way to know is testing. If you feel up to it, go to Home Depot and buy a continuity tester:
Sperry Continuity Tester CT6101 - The Home Depot It will indicate if ground to neutral is connected and if ground to hot is connected; ground to neutral is OK but ground to hot is not and hot to neutral is not but a light bulb plugged in may show there is a problem.
If you decide to check this PLEASE PLEASE PLEASE turn off the main breaker to know with 100% certainty that you are safe to test!
I understand electronics and electrical but not power distribution, hopefully the Engineer is not just saying stuff