Exim has a headers_remove option which can be used in the transport section of your configuration.

If the transport section has:
 
ses_smtp:
  driver = smtp
  port = 25
  hosts_require_auth = $host_address
  hosts_require_tls = $host_address


Add the following line to the end:

headers_remove = X-SA-Exim-Connect-IP:X-SA-Exim-Mail-From:X-SA-Exim-Scanned:X-SES-Outgoing:

Update the config with update-exim4.conf and reload exim4.