You have to keep index at 0, because when you remove, items are updated.
Without any problem, you can delete children and expandable icon will be invisible.
Cheers,
var treeview = $("#ctrlSkillsTree-Destination").data("kendoTreeView");
if (treeview)
{
ctrlSkillsTree.RemoveCheckedItems(treeview, treeview.dataSource.view());
}