Hiding SMTP error messages

Hey Guys, bit of a strange situation we have going on with our email systems… long and short of it is that our email is hosted by Google Apps, so even though the email addresses we use on our site to send customer notifications are valid, because they are hosted off of our server, customers are seeing SMTP errors when placing orders, leading them to believe the orders are being declined :(

Everything is working great minus these errors - orders come through, notifications get sent out, and everything flows as it should, but some of our customers are worried they are getting declined and double ordering.

We’re looking for the quick and dirty solution - to hide SMTP errors… could someone advise us on how to do this?