If deleted products keep showing up in your search after reindexing, please make sure that the latest version of the extension is installed. If the extension is below version 1.6.0, an issue can arise when directly changing products in the database. Because no Magento hooks are triggered when manipulating the database directly, the extension could not recognize that a product was deleted/edited. Version 1.6.0 contains a fix for this issue, so please update the extension if needed.
Please note as Magento no longer supports Magento1, we have stopped development and support on our own Magento1 extension. Therefore, we strongly recommend that you upgrade to Magento2 and the latest version of our extension.