Normally, you should not remove the state information as reported on your W-2 form. The state taxes paid may be deductible on your federal return, and you may have to report them on a tax return for the state listed.
That being said, since New Jersey and Pennsylvania are reciprocal states, you should not have had taxes withheld from Pennsylvania as reported in box 17 or 19. If you did, then you can file a return in Pennsylvania to get a refund of those taxes.
You should include the entire wage amount (box 1) on your New Jersey tax return since that is your resident state. Hopefully, it is reported correctly on your W-2 form in box 16 for NJ. If not, you will have an option to reflect your full wages as belonging to New Jersey when you go through the state tax return in TurboTax. In either case, I suggest you enter the W-2 in TurboTax the way it is printed on the form.