The row is removed at the client side but the list is stored server-side. You need a web method in your server side code that takes the ID and removed that movie from the list.
I would rebuild the table from the server-side response instead of just removing the client-side row. This better allows you to handle and errors and shows an updated table showing all users changes (which I guess is what you would want?).
All of this can be called from the client side using jQuery ajax calls (other client side service calls are available). The
jQuery website can get you started but there are plenty of resources out there.
By default jQuery ajax calls occur asynchronously. If you're response contains data that you wish to pass you can either do this within the ,Success : function(data){} method or call the web service with the ajax parameter ,async: false.
Hope that helps