My guess (and it's only a guess) is that while the geo is running the pump pressure is fluctuating up and down causing water to move back and forth across the meter. For it to do that, there has to be some room for expansion on the soft side, perhaps an expansion tank for the hot water or lots of PEX lines.
Monitor the pressure while the geo is running to see if it is fluctuating.
If you put in a checkvalve then you need to have an expansion tank after it.
That's my guess now as well. Have you actually watched the pressure gauge at the pressure tank while this is going on? Is there a solenoid valve in the geo lines anywhere to isolate all the geo plumbing from the rest of the world when the geo is off? I wonder if you need a check valve in the geo dump line pointing to the well.