It gets us a little closer, but the document is bizarrely formatted using assorted tables, with different numbers of columns in the rows. Even on a basic level such tables are difficult to handle.
However, as you originally identified, the only thing you can really hang the code on here is the size of the graphics. If we can assume all the graphics to be removed have the same sizes then the following macro may work, but without the document to test against the results may be unpredictable because of the table format:
Code:
Sub DeleteImages()
Dim oShape As InlineShape
Dim oRng As Range
For Each oShape In ActiveDocument.InlineShapes
If oShape.Height = 24 And oShape.Width = 24 Then
Set oRng = oShape.Range
oRng.Rows(1).Delete
End If
Next oShape
End Sub