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Also, it is important to note that you cannot put any additional mail transport appliances between Exchange Online and the Exchange on-premises hub or transport servers used for hybrid routing between on-premises and Office 365. Doing so strips the Exchange verbs used in message headers. If an additional mail transport is required, be prepared to install Exchange edge servers.

From

Cover of Microsoft Office 365 Administration Inside Out (Includes Current Book Service), Second Edition

Note

verbs are essentially commands:
Under ESMTP, the EHLO greeting will trigger a response which will list ESMTP keywords. Basically this details what features the SMTP mail server supports. Such features may also have 'verbs' (or commands) associated with them that are used during the SMTP conversation.
http://smtpfilter.sourceforge.net/esmtp.html