Can 4.3 update notification be removed?
Try disabling the notification then restart your tablet and see if it reappears:


  Go to Settings &gt; Application Manager &gt; All &gt; Google Services Framework and then uncheck "Show notifications".


Are you rooted? If so, and if disabling the notification doesn't work, try freezing or uninstalling the update apk:


  Use Root Explorer or ES Explorer and go to phone memory system/app/ and delete or rename UpdateCenter.apk. Alternatively, you could freeze this application in Titanium backup application.


You could also try modifying your build.prop file to trick the tablet into thinking it's already updated (root required). This was also mentioned in an answer to a previous question.


  To prevent the update notification, you will probably just have to
  change the build.prop values. So, change:
  
  ro.build.description=voles-user 2.2.2 FRG83G 91102 release keys to
  
  ro.build.description=voles-user 2.2.3 FRK76 185902 release keys
  
  and
  
  ro.build.fingerprint=verizon/voles/sholes/sholes:2.2.2/FRG83G/91102:user/release-keys to
  
  ro.build.fingerprint=verizon/voles/sholes/sholes:2.2.3/FRK76/185902:user/release-keys


Note that this quote is referring to old software versions and that the ro.build.description and ro.build.fingerprint lines will need to look different for you than those quoted. Check out this answer for more information on making such a change.

For me and my 2012 N7 I just lived with the notification until I couldn't stand it any more, then I just upgraded anyway.