If you have set up email forwarding in Office 365 to forward emails to your BrightManager account you may receive undeliverable emails from Microsoft if you haven't enabled external forwarding on your Office 365 account. The undeliverable email will look like this:
To stop receiving these bounce back messages you will need to enable external forwarding in your Microsoft account, this setting is turned on by default by Microsoft.
If you are unable to adjust this setting you will need to contact your account administrator, or the reseller (for example Go Daddy), you purchased your Office 365 package from.
Log in to Office 365 at https://security.microsoft.com/ and choose Email & Collaboration > Policies & rules > Threat Policies > Anti-spam
Or head directly to the Anti-spam settings page here: https://security.microsoft.com/antispam Note that the policies you see in your own admin may differ from those shown here, as these are only the default policies.

Click on Anti-spam outbound policy (Default) and scroll to click the Edit protection settings link at the bottom of the sidebar
Find the section called Forwarding Rules, and the dropdown list called Automatic Forwarding Rules. Pull that list down and choose On - Forwarding is enabled. Click Save at the bottom. 
To get emails sent from Outlook to appear in BrightManager, ensure that you have created an auto-forwarding rule within your Outlook settings. This involves setting up a rule to forward a copy of incoming emails to the desired email address associated with BrightManager. Without this rule, emails sent from Outlook will not automatically appear on the Client timeline in BrightManager.
If you have cancelled your BrightManager subscription but are still receiving BrightManager-related undeliverable messages or forwarded emails, this usually indicates that a forwarding rule remains active in your email provider.How to stop them
- In your email provider (for example, Outlook/Office 365 Rules or Gmail Filters/Forwarding), locate and delete the rule that forwards mail to your BrightManager forwarding address.
- If your organization manages mail centrally, ask your IT administrator to remove the forwarding rule.
Note: Forwarding rules are controlled in your email system; BrightManager cannot remove them on your behalf.