How do you remove the iOS 9.0.2 Software Update notification pop-up?

Yes there is a way to disable it. First let me explain why you are getting that notification. Even if you have automatic updates turned off, the new IOS update still downloads to your phone and iPad. It is already in your phone and iPad right now waiting for you to completely install it. It is not installed but it is sitting there in your phone and iPad waiting for you to click on it to install. So what you must do is the following:

On the iPad Air 2, Click on the Setting icon. Then click on General. click on Storage & iCloud usage. It might just say Storage on your device. When the next page pops up you will see at the top the word Storage. Under it you will see Manage Storage. Click on it and wait till the list is fully populated. Depending on how many apps you have this can take a couple of seconds to about half a minute. Look through this list till you see the new iOS update. Delete it. Then your pop up notice should go away. Don't worry about loosing the update. You can always get it later in the future. If in the future you get the pop up again, then that means Apple has again downloaded it to your phone or iPad without your permission. Simply do the above all over again to delete it and get rid of the new pop up. This is the only way to get rid of the pop up without installing it.

OS updates are pushed automatically and there is no way to stop this from happening. They push the update when your unit is plugged in and you aren't using it for a period of time.