No you do not need to amend the 2020 tax return that was filed to receive the unemployment compensation exclusion tax refund.
The IRS is in the process of calculating the tax refund for those that are eligible.
Go to this IRS website for information - https://www.irs.gov/newsroom/irs-sending-more-than-2-point-8-million-refunds-to-those-who-already-pa...
however, if you have a state income tax see this link for what to do. some states do require an amended return.