My W-2 has NJ FLI in box 15... I'm going to enter it in Box 14... do I leave Box 15 as is, or remove the FLI portion?

If you have a NJ FLI line in Box 15, this sounds like the payroll company didn't report this correctly.  I agree that you should enter it in Box 14, and be prepared to share with the state how the W2 was prepared if they ask.

Should I remove FLI from Box 15, or leave it as it is?

Yes.  FLI in Box 15 won't pass e-file diagnostics.  You will need to put it into Box 14 in TurboTax to be properly reported to the state.  But if the state later questions it, you can send them a copy of your W2 showing the way how it was reported to you.

leftmost Box 15 must be one of the 50 states.