Installed a dedicated 20 amp. GFCI circuit in kitchen. Used GFCI breaker in panel. Inspector tested it with plug in circuit tester and it did not trip.
You could ask the inspector if you can measure the resistance of his tester from the hot to ground pins when the button is pushed. Then measure the voltage from hot to neutral at the receptacle. Using Ohm's law, the current drawn by the tester with the button pushed is the voltage divided by the resistance. Make sure that the result is at least 6 mA, or the inspector's tester could indicate that a good GFCI is bad.
I have two plug-in testers, and one measures 16.57KΩ and the other 18.66KΩ with the buttons pressed. At 120V they would then draw 7.24 mA and 6.43 mA respectively. The 18.66KΩ seems a little marginal because the voltage only has to drop to 112V to lower the current down to the 6mA level.
According to the UL 943 standard the maximum time allowed before a GFCI trips is T = (20/
I)
1.43 where T is in seconds and
I is in milliamps.
Therefore at 6 mA T can be as long as 5.6 seconds, at 8 mA 3.7 seconds, etc. And so the inspector needs to keep the button pressed for at least 5.6 seconds before he can say that it fails. Of course as we all know, the button on the breaker is the only valid test anyway.