This is how it works for me. In document ready function I assign converted version of HTML table to a variable and when a button in the is clicked I go through parents/childs with JQuery and send the row you get as a parameter to the library's fnDeleteRow() function.
Here's is the comments from the library function. And an example that's mentioned in library.
/**
* Remove a row for the table
* @param {mixed} target The index of the row from aoData to be deleted, or
* the TR element you want to delete
* @param {function|null} [callBack] Callback function
* @param {bool} [redraw=true] Redraw the table or not
* @returns {array} The row that was deleted
* @dtopt API
* @deprecated Since v1.10
*
* @example
* $(document).ready(function() {
* var oTable = $('#example').dataTable();
*
* // Immediately remove the first row
* oTable.fnDeleteRow( 0 );
* } );
*/
// And here's how it worked for me.
var oTable;
$("document").ready(function () {
oTable = $("#myTable").dataTable();
});
//Remove/Delete button's click.
$("a[name='deleteColumn']").click(function () {
var $row = $(this).parent().parent();
oTable.fnDeleteRow($row);
});