Installed a three way with a pilot light, three way switch works correctly, however pilot light never turns off. Whenever basement light is off the pilot should be off.

What is the make and model number of the pilot switch?

We are using Legrand 695-w three way with pilot
Sorry for the delay in answering

Were wiring instructions provided with switch. Does literature specify that pilot light is lit only when switch is on? I could not find wiring instructions or specifications on internet. Do you have a neutral at the switch location. If so, I suggest replacing with a Leviton 3-way with pilot light.

Where is power being fed to, the switch with pilot light or the one in the basement? I suspect the neon pilot light which pulls 1/25 watt or .002 amps is using the ground for neutral. Temporarily remove ground from pilot light switch and see if light goes out. If it does and power is being fed to the pilot light switch, that would mean that to work properly, power would have to be fed to basement switch or to the fixture.

"basement light is off the pilot should be off." this is not right, pilots should be ON if the lights are OFF. Did you mistype?

"basement light is off the pilot should be off." this is not right, pilots should be ON if the lights are OFF. Did you mistype?

No, the application is light on with pilot light on, light off and pilot light off.

Have you tried disconnecting the ground wire as suggested, to see what happens ?