Duplicate messages are received in your Inbox whilst Mimecast for Outlook is operating in Continuity Mode.
Mimecast's continuity logic matches messages in the Mimecast mailbox to those in your Exchange environment. If you are using third party software that modifies incoming mail so that it is different to Mimecast and Mimecast for Outlook, we will not be able to match these messages. In this instance we see them as unique messages, hence the duplication.
Manually move the duplicated messages to the appropriate folders during the Continuity Event. Mailbox rules that move items out of the Inbox may not work during Mimecast for Outlook Continuity Mode. This is because many of these rules are applied by the Exchange server and are therefore not available during an Exchange outage, which is typically the reason to induce Continuity Mode.