I hope you had got answered of your queries , happy for you on this.
It seems you want to customize parent template on child theme, then please follow this steps:
1> First create partial folder inside child theme [Go to site folder -> wp-content -> themes -> puresimple-child-> create partials folder]
2> Create file named logo-group.php and paste your code on this file from parent file. for this [Go to site folder -> wp-content -> themes -> puresimple-> partials -> logo-group.php]
3> Then you can re-undo your changes from parent theme.
4> finally activate your child theme.
Note: A child is just inherits page template but you need re set the setting or value of customizer
Let us know if you are understanding fully or perhaps this not what you meant for.