Parse the code through naked eyes. That is the way out.
Check the url on the browser (and if the UI is loaded asynchronously and partially, the url won't be right"). The url can give you the controller and the action methods which will help you reach the code faster.
If the url is like this - http://servername/Invitations/Client/45 then "Invitations" refer to the controller, and "Client" refers to the action. So search for InvitationsController.cs and the action method "Client" inside that.
The action method will return ActionResult. This would most probably be a View. Check the View, and you will have the markup for the Grid. Once you have the markup, it shouldn't take more than few minutes to alter the markup and get the id.
Hope this helps.