Important to realize, all the updates of any theme occur within the WordPress Admin Panel. So, when you try to get an update for our theme, it needs to connect with our servers. And if the connection gets any newest version/files in our servers, it will display the new update available into your WordPress dashboard. Here, you are asked if you want the update. If the answer is positive, it needs the write permission to copy the files into certain folders of WP content.
Now, using FTP first locate the above folder, then with right-click on the folder, go to Properties and check on the write (W) permissions.