Been working on this a while. First: root the phone. There are ways to do this,
go into the running applications and find the source of this stuff, it's either or both 'software update' and 'security policy update' ...force close them, wipe their process, whatever you can do ... this is probably temporary.
Next for the permanent stuff
1st method (froze my phone): is from qbking77 (google it) and a file 'CF-Auto-Root-hltespr-hltespr-smn900p.tar' contained in a zip file including a newer version of Odin3 v3 or something like that. This got me stuck. But maybe I forgot a step (like enable usb debugging)
2nd method (worked for me after first method froze my phone) using an older version of Odin3 v1.85 with a file CF-Auto-Root-hlte-hltexx-smn9005.tar
The latter worked for me after the former got me stuck. You can try the first and see if it's a go ... because phones can be a tad different. If you get stuck do the 2nd method same procedure and you're fine.
Now that you're root (have some guts and root, it's worth it)
Get titanium back up and freeze the process "software update". You can even look at the details of the file and find the name of it and where it is. I didn't delete, I just froze it to be safe. Also freeze "security policy update". This is probably making the phone secure from you being able to do what you want.
Get esfile explorer with root add on for the following ...More steps, in addition to this .. which may be exessive ...(but hey, I want to be vigilant about stopping that 4.4 software from locking down all my freedoms)
HOW TO] Disable OTA Update (G-Note 3) Notifications!!!!!!!!!!!!!
The user lordazoroth originally posted this method here in the T-Mobile SGSIII forum. However, I have confirmed that it works with the Note 3 (at least with the Verizon variant) with one small difference. Feel free to give us both a "THANKS" if this helped you out.
You can disable the OTA Update notification by following the steps below. Just be aware that there is a small change in STEP #3.
Step 1. Delete the update located in /cache/fota/ (may be /data/fota) and then click the update notification prompt to install it, it will instantly fail and the notification will disappear. (My phone rebooted and tried to install the update - this is the point where my Note 3 gave the update failed notification. I just rebooted the phone and went to STEP #2.)
Step 2. Disable otacerts.zip located in /etc/security by renaming it to otacerts.zip.bak
Step 3. Disable FotaClient.apk and FWUpgrade.apk by renaming with .bak extensions located in /system/app/
Step 4. Reboot
(NOTE: The difference in STEP #3 for the Galaxy Note 3 is that the [FotaClient.apk] is named [LocalFotaClient.apk] instead of just [FotaClient.apk]. All of the other steps are the same.
Continue running JB 4.3 and enjoy your Note 3 without that nagging update notification!
I'm not an expert, but I do know that when they updated my note 2 with all this kitkrap they messed up my stuff. Power user no more. Couldn't move files, couldn't even get picture messages on gosms. I had a really tough time rooting it back and re-installing whompasaurus.