Does Gravity Forms show a renewal message in the Admin Notification email (not the User Notification) if you have an expired license key? Yes.
But you are incorrect that it can't be removed, and this has already been explained to you via email when you attempted to enlist Joost de Valk in some sort of campaign to damage our reputation. But you left that part out, primarily because Joost had no problems with how we handle the license expiration message once it was explained.
Removing this renewal message is simple: remove your license key from the settings page of Gravity Forms. Problem solved.
An expired key is an expired key, so disabling the message while you have an expired key entered isn't possible without editing code… which you are free to do of course because it's GPL. HOWEVER removing the license key means you have no license key, so there isn't going to be a message about an expired license key. There won't be any message because you wouldn't have a key. If your key is expired and you don't want to renew it, then there is no reason to have it entered on your Settings page.
The message in the Admin Notification is one of the ways we try to get out in front of users to make sure they are aware that their license key has expired and give them an opportunity to renew. We provide users with a substantial discount to renew their license, but only for the first 60 days after the key expires.
We try to give users every opportunity to renew, in order to do that we need to be able to make them aware that the license has expired. The notice in the Admin Notification (NOT the User Notification) is one of the ways we do this. Relying on the user logging going to the Settings page of Gravity Forms isn't the most efficient means of notifying them... they may never go to the Settings page again after they initially install Gravity Forms.
Wouldn't you be upset if you wanted to renew your license at a 50% discount (for Developer and Business Licenses) but weren't aware your license had expired and now you are out of the 60 day discounted renewal period so you can't get the 50% discount anymore?
Again, to get rid of this "nag" is simple... remove your license key from the settings page.
Your comment that you don't nee software updates is entirely a personal choice. But I will say that it isn't a good one to make. A perfect example is the release of WordPress 3.2. WordPress changed the version of jQuery that comes bundled with WordPress. This change made older versions of Gravity Forms incompatible with WordPress 3.2 and require us to release updates to resolve this issue prior to the release of WordPress 3.2. There is a lot of value in having access to software updates because we don't control WordPress so sometimes we have to release updates to ensure compatibility with new releases.
So if you don't renew your license key and WordPress releases an update that changes core functionality… you may not be able to update your version of Gravity Forms to ensure compatibility unless you have a valid license key.
We provide users with a substantial discount when they renew. It's a small price to pay to ensure Gravity Forms will continue to work with each new WordPress release.