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Exchange 365 deleting large mails within a date range

Somtimes a retention policy isn't enough, can't use it or you simply just need to run it once in your lifetime. 

You need the Powershell Exchange module installed to be able to do this.
Try running Connect-ExchangeOnline and see if you can connect, if you can't, you need the module.
Install it using Install-Module -Name ExchangeOnlineManagement

Once connected to your tenant, you need to run the following command to delete e-mails
Get-Mailbox -Identity "marioatitsme.com" | Search-Mailbox -SearchQuery {((Received -lt '01/01/2010') -and (Received -ge '01/01/2021')) -and ("Size:5000000..31457280")} -DeleteContent

The size is in bytes, so if you want to delete mails starting at 5MB and larger convert 5MB to bytes. 
I believe the dates also have to be filled in the american way, month/day/year.