You mean, that you want to put a Toolset Form (Former Toolset CRED) into that Pop Up that appears when you click on some of those links in the table?
That can be possible, but you need to put the Toolset ShortCode for the Form in an editor that can expand it, such as a Content Template for example.
The third-party code you share doesn't really tell much about how the WordPress query is made and how data is collected and presented, and it's not subject to support analysing that.
But you could create such a table with Toolset Views and insert the Form ShortCode in a Bootstrap 3 Modal, for example, which appears once you click a certain link or button.
This is perfectly possible with Toolset alone, but if you require displaying CRED forms in other outputs, this is not a problem.
It just needs to either an editor that somehow can expand the ShortCode and you can call in a modal, or you call the form with PHP, but then you need to observe this issue here:
https://toolset.com/errata/unexpected-input-when-shortcode-with-id-attribute-is-rendered-using-php/
In Toolset Forms, this above Errata translates to:
- In a CRED Form holding a [wpv-post-title id='$parent_post_type_slug']") ShortCode, rendered via PHP (echo (do_shortcode("[cred_form form='YOUR-FORM-ID']")); ), this shortcode fails to load the correct parent.
Of course, that is an exception that does only happen if you plan to work with attributes in shortcodes like above shown.
Generally, it's not recommended to output Toolset Forms via PHP.
Hence you would be left with inserting the Shortcode in some HTML editor, for example, a Content Template, or Post Body, or where your 3rd Party Plugin builds the HTML output.
However, we cannot assist the 3rd Party Plugin.
The authors of the Plugin, however, can always join the "Beyond Pages" Programme, which allows integrating Plugins and Themes with Toolset:
https://toolset.com/documentation/beyond-pages-program/
Or, if you find compatibility issues between Toolset and that plugin we are always ready to help solving those together with the authors of the 3rd party Software.