In general, you don't need to amend your return to report Roth IRA contribution, as it makes no impact on your tax return.
However, you may want to go through the amendment process, though, just to check if you may qualify for the Retirement Savings contribution credit and if that will change your refund. Also, if you amend and enter the contributions, TurboTax will help you keep track of your Roth basis. No need to send anything to the IRS, but you will keep the Roth contributions worksheet with your records. Here are amending instructions.