It is quite easy to unlock the T-Mobile Note 3. All you have to do is download Towel Root from towelroot.com and then root your Note 3 if it is not already rooted. After you root it, Download supersu from Google Playstore and open SuperSu to update the binaries. Supersu will ask you if you want to disable Knox, I said Yes because I hate Knox. After you do this, go to Google.com on your Note 3 browser and type “Chainfire Region Unlock apk” and you should see the XDA Forum post by Chainfire who will allow you to freely download his Region Unlock app but if you feel like buying him a beer, go to the Google Playstore and download his Chainfire region unlock app from there for a small fee of like $2.99.
After you download Chainfire’s Region unlock. Go open the app and give it Super User access. It will allow you to region unlock your Note 3. Restart your phone and you are now unlocked for the whole world.