Remove action of an external plugin after checking if custom post meta is set

According to the documentation for remove_action() the function name and priority must match the usage where the function was hooked. You have made a common sense assumption that a higher priority should be used for the removal but I believe that is the cause of the problem.

Docs:
https://developer.wordpress.org/reference/functions/remove_action/

To remove a hook, the $function_to_remove and $priority arguments must match when the hook was added. This goes for both filters and actions. No warning will be given on removal failure.

Update your remove action statement to explicitly define a priority of 10:

remove_action( 'wp_footer', array('External_Plugin','inject-code', 10 ) );