THERE IS NO SUCH THING AS A NJ EXIT TAX. (Repeat over and over until you get it right.)

It is a non resident withholding which must be reported and filed on either a NJ 1040 NR or part year NJ 1040 if the TP qualified for the IRC Sec. 121 exclusion.

THEN you get the money refunded. Be certain to enter the withheld tax on the correct line as "tax witheld on real estate sale" or whatever it says or NJ will not refund it.