Yes, you will want to remove the NY box 16 amount in your NJ state interview. In the NJ step-by-step interview you will arrive at a page asking you to confirm the NJ taxable wages for the employer that has two states lines. Both box 16 amounts will be listed and you should check the box to remove the NY box 16 amount.
In the NY state step-by-step interview in the "Credits" section using the "Credit for taxes paid to another state" topic you will enter the NJ box 16 amount when asked about the NJ taxed wages.
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