Your parents will have to mail their return this year. They don't have to wait for you to amend. You will have to amend your return to say you can be claimed on someone else's return. It will take 8-12 weeks to process an amended return if not longer. In the meantime you will probably each get a letter from the IRS to determine who is able to claim the exemption.
Read this on how to amend a current year return
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/amend-federal-tax-return-current-year/L7eS6o1qh_US_en_US?uid=lfunevhk