Mail flow from an Office 365 environment to a Domino user calendar appointments show as WINMAIL.DAT.
This environment was configured in a hybrid mode with both local Exchange and Office 365, with remote domains configured.
This was caused by the value set to "Always use" for "Exchange rich-text format" on the "Message Format" tab of the remote domain configured for Domino.
Please change this value to "Never use" using the Exchange Management Console and once replication to Office 365 has completed please test this again to verify this resolved this issue.
The following Microsoft Technet provides more detail on setting the Message Format for non-Exchange based mail systems.
To change this:
Open the Exchange Management Console | expand "Organization Configuration" | "Hub Transport" | select the "Remote Domains" tab | select and right click and choose properties of the correct Remote Domain | select the "Message Format" tab | select "Never use" | click apply and OK.