Child Plugin Admin Panel

I’m assuming you’re asking how to remove the first action, which the plugin has created?

Removing an action is really easy – all you need to do is call remove_action like this:

remove_action("admin_init", "backend_plugin_css_scripts_mail_bank");

Then add your replacement action.

You need to ensure that you remove the action after it has been added (because otherwise there’s nothing to remove!) and before the admin_init hook runs (otherwise the action you wanted to remove would have already run). For further information on which hooks run in which order, you can see https://codex.wordpress.org/Plugin_API/Action_Reference (or Google for another appropriate reference).