For Windows Personal computer and Windows Servers, Internet Explorer shows up in Control Panel, Programs and Features, Windows Features. Open Windows Features.
It is there in Personal Computers with Windows 10 and back to at least XP if not before.
IE could be enabled on Server 2012 and servers prior so certainly Server 2008.
In a standard Native setup (not hacked in some way), Internet Explorer could not be completely and totally uninstalled.
It could be disabled in Windows Features but basic elements of IE would remain as these were built into the operating system.
In your case IE may have already been disable in Windows Features. if it cannot be enabled (nothing there to enable), then your system may have been hacked a registry change or there may be some other issue.
So then, since Server 2008 is so long out of support, there is (a) nothing you can do or (b) contact Microsoft Support (you say an extra 3 years of support was added) but remember Microsoft will more than likely charge you for the service.
If your Server is otherwise operating properly, there is no "need" to uninstall IE - it does not cause issues in a Native, properly operating server.