Sometimes the state refund you received includes amounts that are not really refunds of state income tax, and are therefore not reported as income on your federal tax return the following year. For New York specifically, such amounts include "certain refundable credits, such as the empire state child credit, real property tax credit, earned income credit, child and dependent care credit, farmer’s school tax credit, and the New York City school tax credit," and also interest paid by New York State on an overpayment. If you got any of those credits on your 2016 New York return, that probably explains the difference in the refund amount.
The amount that you see "populated" on the TurboTax entry screen is the total refund, after subtracting the credits listed above, but before the calculation of the taxable amount that is affected by your other deductions, etc. The amount that is entered in TurboTax should match the amount on your Form 1099-G from the state. You can access your Form 1099-G at the following link on the New York State Department of Taxation and Finance web site.
https://www.tax.ny.gov/pit/file/1099g.htm
Whatever amount you enter in your federal tax return, it will not affect your state tax return because the state refund is not included in your New York income. It gets subtracted out on the New York return.
