1.) Download a backup:
Using FTP like filezilla, login to your server and then go to this folder: /wp-content/themes. From there, download the entire child theme folder: x-child-integrity-light on to your computer. That will be your backup. After that, feel free to remove/delete x-child-integrity-light from here: /wp-content/themes.
2.) From the #1, we delete already current child theme. Now we have to install the latest one. See this guide: https://theme.co/apex/forum/t/setup-how-to-setup-child-themes/57
3.) Doing #2 means you now have the latest child theme structure x-child folder with no customization yet. Now from the backup we did on #1, inside the x-child, there's style.css and functions.php file in there. Copy your customization you have from the backup to the files on the new child theme. Do this on all other custom templates too. There's some structure changes on header and footer so make sure to take that into account. To do that, just check the files location you have customized from the parent X theme.
Hope this helps.