Except for special categories ( like the NY 414h category) the box 14 entries are informational and do not affect tax calculations. This is true for NJ as referenced here.
In this case your NJ 414h box 14 entry is informational only and does not affect your NJ taxes because the contribution has already been excluded from box 1 wages.
Therefore to allow the NY efile you should not enter the NJ414h box 14 line into TurboTax at all.
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