Yes, having Box 7 filled in can hurt you. As @ColeenD3 suggested, you will want to request a corrected 1099-NEC from your client. That box indicates that this income would be taxable by Connecticut, which means you would have to fill out a nonresident return for Connecticut and pay state income taxes on the amount you received from this client less any expenses.
This is not true, as Connecticut will not tax New Hampshire telecommuters who did not perform any of the work within Connecticut. Box 7 should be left blank for you.
