Remote Server returned '550 5.7.705 Access denied, tenant has exceeded threshold.

claireturner 

Base on the error message, it seems Exchange Online Protection (EOP) filters identify a very large volume of suspicious email coming from your tenant and triggers a block of outgoing email action
Several different reasons may occur, please make sure your Exchange in terms of SPAM and report to Microsoft to unlock

Get support - Microsoft 365 admin | Microsoft Learn

Hi claireturner 

https://learn.microsoft.com/en-us/microsoft-365/security/office-365-security/removing-user-from-restricted-users-portal-after-spam?view=o365-worldwide

Please refer to this documentation