Awesome Tax Expert @LenaH is correct. Do not remove your New Jersey wages. NJ receives a copy of your W-2 and will be looking for the NJ Box 16 amount, not your NY amount.
The duplicate wages are not related to the credit for taxes paid to NY. New Jersey will give you credit for the appropriate income and tax reported on the NY return.
Connecticut and Michigan have completely different tax systems than NJ. New Jersey does not use federal income which is why you NJ wages generally do not match Box 1 federal.
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