Word – All table borders on Word document erased

Create a macro in Word using the following code:

Sub SelectAllTables()
    Dim tbl As Table
    Application.ScreenUpdating = False
    For Each tbl In ActiveDocument.Tables
        tbl.Range.Editors.Add wdEditorEveryone
    Next
    ActiveDocument.SelectAllEditableRanges (wdEditorEveryone)
    ActiveDocument.DeleteAllEditableRanges (wdEditorEveryone)
    Application.ScreenUpdating = True
End Sub

Run the macro to select all tables, then you can modify their borders in one go:

Edit: Ok, this should be able to recursively handle nested tables as well to any level:

Sub SelectAllTables()
    Dim tbl As Table
    For Each tbl In ActiveDocument.Tables
        DelTableBorder tbl
    Next
End Sub

Function DelTableBorder(tbl As Table)
    Dim itbl As Table
    tbl.Borders(wdBorderLeft).Visible = False
    tbl.Borders(wdBorderRight).Visible = False
    tbl.Borders(wdBorderTop).Visible = False
    tbl.Borders(wdBorderBottom).Visible = False
    tbl.Borders(wdBorderVertical).Visible = False
    tbl.Borders(wdBorderHorizontal).Visible = False
    tbl.Borders(wdBorderDiagonalUp).Visible = False
    tbl.Borders(wdBorderDiagonalDown).Visible = False
    For Each itbl In tbl.Tables
        DelTableBorder itbl
    Next
End Function

More than likely you have opened a document with restricted editing. Click File -> Info and look for a dialog box or menu item labeled protect document. It should display a message if the document is restricted in some way. Unless you are the original document creator you likely won't be able to un-restrict the document, you'll need to create a new one.