type
  TCheckListBoxHelper = class helper for Vcl.CheckLst.TCheckListBox
  public
    procedure GetCheckedItems(List: TStringList);
  end;

implementation

{ TCheckListBoxEx }

procedure TCheckListBoxHelper.GetCheckedItems(List: TStringList);
var
  I: Integer;
begin
  List.Clear;
  for I := 0 to Items.Count - 1 do
    if Checked[I] then
      List.Add(Items[I]);
end;

procedure TForm1.Button1Click(Sender: TObject);
var
  CheckedItems: TStringList;
begin
  CheckedItems := TStringList.Create;
  try
    CheckListBox1.GetCheckedItems(CheckedItems);
    // so something with CheckedItems
  finally
    CheckedItems.Free;
  end;
end;