Sorry I don't understand your question. What does your state refund have to do with the IRS? Are they saying you didn't report your 2013 state refund (you got in 2014) as income?
The IRS is only concerned with your federal return, not your state return. Did the IRS offset your 2018 federal refund for a state tax debt you owed? Sometimes the IRS does seize federal refunds for state taxes that are delinquent. Or do you mean you received a letter from your state saying you owe for tax due on a 2014 return? Do they say they changed something on your 2014 return, or that you did not pay what you owed when you filed the return --presumably in 2015 when it was due? Why do you think it was a TurboTax error? Did you check your own credit/bank records when you filed the 2014 state return to make sure they received your payment?