Then you need to exclude Timeline in this part of response method

if (!$this->_sMetaType && !$aValue['GlobalSearch'])

                continue;

or directly in the __construct in this part:

$this->aClasses = BxDolDb::getInstance()->fromCache('sys_objects_search', 'getAllWithKey',

           'SELECT `ID` as `id`,

                   `Title` as `title`,

                   `ClassName` as `class`,

                   `ClassPath` as `file`,

                   `ObjectName`,

                   `GlobalSearch`

            FROM `sys_objects_search`

            ORDER BY `Order` ASC', 'ObjectName'

        );