سلام.

به این شکل میتونید عمل کنید:

$('.isDone').click(function(e){
    var selectedItem = $(this);
    var selectedItemClass = selectedItem.hasClass('fa-check-square-o') ? 'fa-check-square-o' : 'fa-square-o';
    var parent = selectedItem.parent();
    var tid = $(this).attr('data-taskId');
    $.ajax({
      url : "process/ajaxHandler.php",
      method : "post",
      data : {action: "doneSwitch",taskId : tid},
      success : function(response){
          selectedItem.removeClass(selectedItemClass);
          if(selectedItemClass == 'fa-check-square-o') {
              parent.removeClass('checked');
          } else {
              parent.attr('class', 'checked');
          }
          selectedItem.addClass((selectedItemClass == 'fa-check-square-o') ? 'fa-square-o' : 'fa-check-square-o');
      }
    });
});