This is the link for reference on how to setup SMTP Relaying with Office 365
How to set up a multifunction device or application to send email using Microsoft 365 or Office 365 | Microsoft Docs

If they are using “Direct Send” option, it should not work for sending emails to external addresses like Gmail. Direct Send should only be used to send emails to your own Office 365 tenant. These are the direct send SMTP Settings:

If you want to send emails from Office 365 to External Domains, then they must use either “Authenticated SMTP” or “SMTP Relay”. If you use “Authenticated SMTP”, then they need to make sure the account they use is not blocked to use this protocol. Places to check are:

1. Azure AD Conditional Access or Azure Security Defaults (Azure Active Directory security defaults | Microsoft Docs)
2. Authenticated SMTP on the Mailbox Level via Exchange Admin Centre or Microsoft 365 Admin Centre.

We recommend to use “SMTP Relay” method if they want to email outside of Office 365 and these are the steps they should look into get this working properly and be trusted by external email servers:

1. Add the IP Address to Exchange Connector
2. Add the IP Address to SPF record
3. Enable Dkim in Office 365
4. Have a Dmarc record (Preferably the policy is set to either quarantine or reject)