I tried moving the core folder outside the mantis webroot (as suggested by the admin checks), but it fails with the following error

PHP Fatal error:  require_once(): Failed opening required '/opt/bitnami/mantis/core/constant_inc.php' (include_path='.:/opt/bitnami/php/lib/php') in /opt/bitnami/mantis/core.php on line 69

Checking the core.php file I see the following (line 69)

# Load supplied constants
require_once( dirname( __FILE__ ) . DIRECTORY_SEPARATOR . 'core' . DIRECTORY_SEPARATOR . 'constant_inc.php' );

Note that this path is not using the g_core_path global variable, therefore the issue