Interesting problem - never heard of it yet.
How often do you do the backup?
What you could try is disable the Outlook/Exchange provider while running it.
Either just try pausing the provider, or if this doesn't work, try quitting Outlook, stoping the provider, restarting Outlook and running the backup. That should definitely work as in this scenario, the avast Outlook plugin is not in use at all...
OR - you could just try disabling scanning of already-received mails. Click the avast (a)-ball tray icon, select 'Details >>', double-click Outlook/Exchange and do the change.
Thanks,
Vlk