Sorry - my fault. I usually call the Excel object xlAPP and not objExcel. The code has both references

The following works.
Code:
Private Sub CommandButton1_Click()
Dim objExcel As Object
Dim exWb As Object
Dim rng As Object
Dim c As Object
Dim TaskStatus As String
Dim oTB As Word.InlineShape
Set objExcel = CreateObject("Excel.Application")
Set exWb = objExcel.Workbooks.Open("C:\Temp\File.xlsm")
Set rng = exWb.Sheets("STATUS_DATA").Range("WordID")
For Each c In rng.Cells
TaskStatus = c.Offset(0, 1)
For Each oTB In ActiveDocument.InlineShapes
If oTB.OLEFormat.Object.Name = c Then
oTB.OLEFormat.Object.Text = TaskStatus
Exit For
End If
Next oTB
Next
exWb.Close
objExcel.Quit
'Label1.Caption = "Job task status last updated: " & Date
Set exWb = Nothing
Set objExcel = Nothing
Set rng = Nothing
Set c = Nothing
Set oTB = Nothing
End Sub