@PAToyota That is terrible advice. Doing that, and having a real ground fault in the system, will electrify your water lines. If timed correctly, you can get a nice shock when turning on a faucet, or worse.
You CANNOT ground anything if you don't have a ground wire (EGC, equipment grounding conductor, the typically bare copper wire snaking in and out of each junction box). Don't ground the GFCI. What the inspector found was not a code violation. It's just an old installation, period.
Per NEC 406.4(D)(2)(b), you can install a GFCI device on an ungrounded circuit. It sounds like that is what you have already. That’s better than doing nothing as it does provide personnel protection and some equipment protections too. Install a GFCI as the first device on each circuit you want to protect. You have to label the GFCI ‘No equipment ground’, the same labeling goes for devices downstream but only if they have the third hold for the U ground.
GFCI’s work by monitoring current balance between the line and neutral wires, not by presence of a ground wire. It’s assumed that if there is a current imbalance, current is being lost somewhere in the system, most commonly a ground fault.
Best solution, and the most costly, is pulling in new romex with a ground. Too costly, you're selling, don't bother!
@CSteppe82 If you want a copy of the code section, I'll send it to you.