NJ and PA have a compact so one state doesn't tax residents of the other state. Your client gets all that PA tax back.

NJ law doesn't give a tax credit for taxes paid to another "state." It's another "jurisdiction." That's why NJ residents get a tax credit for Philly wage tax. Philly is another jurisdiction.

NJ gets a credit for the local tax based on the matching income, local wage compared to NJ wage, but not the PA tax, since it is all refunded.