I get this nag notification often. However, I am aware what IT policy I don't have in place. In my case, it is the need for an unlock password on my phone... which I don't want. I know why I should have it, but I don't want it. Please save your breath lecturing me about security.
@OldFatGuy: you need to ask about your IT admin about the specific security policy, not just for your mail server settings.
I've removed and added the account several times, but this doesn't stop the message. It doesn't just appear when I startup, it appears every time a new email arrives. Ugh!
In my case, when I click on the notification, it doesn't even take me to the account settings or phone settings. It doesn't know what to do, so it just goes away. I would still prefer not to be nagged about it all the time.
The workaround for me was to disable email push. I set it to never check--I'll do it manually when I need to check this email remotely.
I suspect many of you will need or want push notifications enabled and I think you're out of luck besides obtaining the correct security settings and implementing them on your phone. Consider yourself lucky that it synchronizes at all without the correct security settings. When Google gets around to making Exchange a priority, you likely won't be able to sync OR your Exchange admin will be able to control many aspects of your phone, including a remote wipe if they so choose.
My ideal (which is probably a couple years away before programmers get around to setting it up this way), would be to require the security policy for the ACCOUNT (managed by the app, but I would accept for the whole APP too since most people don't have Exchange accounts from different orgs), but not for the whole phone. So, if my Admin wants a two factor authentication, then the app can require a password before displaying my email.