We're NJ residents, and all our earned income is from Philadelphia. NJ gives a credit for tax paid to Philadelphia; Turbotax first tells me it's $2,857 but then $2,447.

On one screen I enter the double-taxed income information; how much I earned and how much I paid to Philadelphia.  In the next screen it says, Congratulations your credit is $2,857.  In the screen following that, it summarizes that my tax owed to NJ is $2786 and my credit for taxes paid to other jurisdictions is $2,447.  Why did the credit go down??