Hannah is a California taxpayer. She is retired and receives a pension payment of $$1,000$ during $2022,$ and then in $2023$ receives a letter from the pension administrator informing her that an internal audit of the pension computer system revealed that the administrator made a mistake and overpaid the $$1,000$ benefit in $2022.$ As such, they now want Hannah to repay $($the $$1,000$ overpayment$)$ by writing a check back to the pension plan in $2023.$ Under Section $1341,$ Claim of Right, Hannah is entitled to claim a deduction for what amount of the overpayment on her California income tax return for tax year $2023?$

A$.$ $$500$

B$.$ $$600$

C$.$ $$1,000$

D$.$ $$3,000$