During a recent migration project, we migrated several mailboxes to Office 365 using the staged migration approach. Naturally, during the migration, users that had been migrated still sent meeting invites to on-premises users and meeting rooms. The problem was that meeting invites were actually received as clear text and stripped of the necessary attributes that make it a meeting request. The on-premises server was Exchange Server 2003 SP2.

As you might know, during a staged migration, DirSync creates MEUs (mail-enabled users) in the cloud. These MEUs actually represent on-premises users that have not been migrated yet and they make sure that the global address list in Office 365 matches the on-premises global address list.

When a user with a cloud mailbox sends a meeting invite to an on-premises user, he actually sends the invite to the MEU. The MEU has a TargetAddress that points back to the on-premises user. The MEU also has settings that control how mail should be formatted when sent to the actual on-premises user. The solution to the problem was to change the UseMapiRichTextFormat  to a value of Never using the following PowerShell command:

set-MailUser MEUname -UseMapiRichTextFormat Never

For all MailUser objects, use:

get-mailuser | set-MailUser -UseMapiRichTextFormat Never

After running this command, cloud users could successfully send meeting requests to on-premises users. Hope it helps!