The Caption property refers to the Application Title Bar rather than a caption within a document. (See https://msdn.microsoft.com/VBA/Word-VBA/articles/application-caption-property-word)
I can't find any way to directly refer to captions within a document. However, captions are stored within a document using fields, so you can access them using the Fields collection. Specifically, a Sequence (SEQ) field is used to generate the number. The rest of the caption is just text.
To find the captions, you can loop through all the fields in the document and identify which are Sequence fields. You may have other types of captions eg for figures, so use the Code property to get the full text of the field and check whether it's for a table. You'll then need to identify the paragraph containing this field and delete it.
Here's a sample:
Sub Delete_Table_Captions()
Application.ScreenUpdating = False
Dim i As Long
With ActiveDocument
For i = .Fields.Count To 1 Step -1
Dim f As Field
Set f = .Fields(i)
If f.Type = wdFieldSequence Then
Dim s As String
s = f.Code.Text
If InStr(1, s, "Table", vbTextCompare) > 0 Then
f.Code.Paragraphs(1).Range.Text = ""
End If
End If
Next
End With
Application.ScreenUpdating = True
End Sub
Note: This just deletes the original caption, so you'll still need to insert the new one. Your example wasn't copying the existing caption text to the new caption, so if you want to do that, you'll need to store the text from the original captions before deleting them and creating the new ones. You can extract the relevant text from Paragraphs(1).Range.Text