"This State" means North Carolina because that link from the state of North Carolina.
North Carolina requires physical presence. You are not subject to North Carolina tax if you do not work in the state.
Even if your employer corrects your W-2 you are probably out of luck. They probably won't adjust your withholding because that's already been paid to the state,
However, if they are able to correct your state wages, that will keep you from writing a bunch of letters if you get audited. You won't owe tax because you reported your income correctly, but you'd still have to respond to a notice.
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