The state does not accept a refund amount and TurboTax does not provide state refunds.
When a return is accepted, that means the IRS or state accepts the identity of the filer. The return is then processed and changes can be made by the state that will alter the refund amount. If they change your refund amount, they will usually send a letter explaining the changes within a couple weeks. The state provides your refund, not TurboTax.