Faça assim

'adicione um  Check

Private Sub Check1_Click()
    If Check1.Value = vbChecked Then
        Dim i As Long
        If lvwBackColour.ListItems.Count > 0 Then
            picBG.Width = lvwBackColour.Width
            picBG.Height = lvwBackColour.ListItems(1).Height * (lvwBackColour.ListItems.Count)
            picBG.ScaleHeight = lvwBackColour.ListItems.Count
            picBG.ScaleWidth = 1
            picBG.DrawWidth = 1
            picBG.Cls
            For i = 1 To lvwBackColour.ListItems.Count
                If (lvwBackColour.ListItems(i).Index Mod 2) = 0 Then
                    lvwBackColour.ListItems(i).Checked = True
                    picBG.Line (0, i - 1)-(1, i), &H4000FF, BF
                    lvwBackColour.ListItems(i).SubItems(3) = "Hidden column value = 1"
                Else
                    lvwBackColour.ListItems(i).Checked = False
                    picBG.Line (0, i - 1)-(1, i), &HFFFFFF, BF
                    lvwBackColour.ListItems(i).SubItems(3) = "Hidden column value = 0"
                End If
            Next i
            lvwBackColour.Picture = picBG.Image
        Else
            picBG.Cls
            lvwBackColour.Picture = picBG.Image
            For i = 1 To lvwBackColour.ListItems.Count
                lvwBackColour.ListItems(i).SubItems(3) = "Hidden column value = 0"
            Next i
        End If
        Check1.Caption = "Remove colouring and empty checkboxes"
    Else
        Check1.Caption = "Make every other row coloured."
        picBG.Cls
        lvwBackColour.Picture = picBG.Image
        For i = 1 To lvwBackColour.ListItems.Count
            lvwBackColour.ListItems(i).Checked = False
            lvwBackColour.ListItems(i).SubItems(4) = 0
            lvwBackColour.ListItems(i).SubItems(3) = "Hidden column value = 0"
        Next i
    End If
End Sub

 

'na propriedade do seu LstV

Private Sub lvwBackColour_ItemCheck(ByVal Item As MSComctlLib.ListItem)
    Dim i As Long
    If Item.Checked = True Then
        lvwBackColour.ListItems(Item.Index).SubItems(4) = 1
    Else
        lvwBackColour.ListItems(Item.Index).SubItems(4) = 0
    End If
    If lvwBackColour.ListItems.Count > 0 Then
        picBG.Width = lvwBackColour.Width
        picBG.Height = lvwBackColour.ListItems(1).Height * (lvwBackColour.ListItems.Count)
        picBG.ScaleHeight = lvwBackColour.ListItems.Count
        picBG.ScaleWidth = 1
        picBG.DrawWidth = 1
        picBG.Cls
        For i = 1 To lvwBackColour.ListItems.Count
            If lvwBackColour.ListItems(i).SubItems(4) = 1 Then
                lvwBackColour.ListItems(i).Checked = True
                picBG.Line (0, i - 1)-(1, i), &H80FFFF, BF
                lvwBackColour.ListItems(i).SubItems(3) = "Hidden column value = 1"
            Else
                lvwBackColour.ListItems(i).Checked = False
                picBG.Line (0, i - 1)-(1, i), &HFFFFFF, BF
                lvwBackColour.ListItems(i).SubItems(3) = "Hidden column value = 0"
            End If
        Next i
        lvwBackColour.Picture = picBG.Image
    Else
        picBG.Cls
        lvwBackColour.Picture = picBG.Image
    End If
End Sub

 

' NÃO QUIZER USAR O Check, use apenas o salto de linha "Rows"