You are correct, you need to do this by your filing deadline (April 15) or any extensions.
"Withdrawal of excess contributions. For purposes of determining excess contributions, any contribution that is withdrawn on or before the due date (including extensions) for filing your tax return for the year is treated as an amount not contributed. This treatment only applies if any earnings on the contributions are also withdrawn. The earnings are considered earned and received in the year the excess contribution was made.
If you timely filed your 2013 tax return without withdrawing a contribution that you made in 2013, you can still have the contribution returned to you within 6 months of the due date of your 2013 tax return, excluding extensions. If you do, file an amended return with “Filed pursuant to section 301.9100-2” written at the top. Report any related earnings on the amended return and include an explanation of the withdrawal. Make any other necessary changes on the amended return.
Applying excess contributions. If contributions to your Roth IRA for a year were more than the limit, you can apply the excess contribution in one year to a later year if the contributions for that later year are less than the maximum allowed for that year."
Hope this helps.
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