I have chosen Deluxe to file federal taxes and confirmed to pay a fee only for federal. Why should I pay a fee ($44.99) for turbotax for filing NJ state taxes?

Using the TurboTax online editions of Deluxe or higher, the state program software is an additional $44.99.  

If you do not want to file a tax state tax return using TurboTax then see this TurboTax support FAQ for deleting the state tax return - https://ttlc.intuit.com/questions/1900608-how-do-i-delete-my-state-return-in-turbotax-online