Your sample documents have manual formatting in the form of pink shading that is at the root of the problem. I would also recommend that you put the code in an add-in template or the normal template rather than a document. The following will remove the formatting from the hyperlinks and adopt the hyperlink styles that are present in the documents.
Code:
Option Explicit
Sub UpdateDocuments3()
'Graham Mayor - https://www.gmayor.com - Last updated - 02 Aug 2023
Dim strFolder As String, strFile As String
Dim wdDoc As Document
Dim oLink As Hyperlink
strFolder = BrowseForFolder("Select folder containing the documents to process")
If strFolder = "" Then Exit Sub
strFile = Dir(strFolder & "*.docx")
While strFile <> ""
Set wdDoc = Documents.Open(FileName:=strFolder & strFile, AddToRecentFiles:=False, Visible:=True)
'Debug.Print strFile
With wdDoc
For Each oLink In .Hyperlinks
oLink.Range.Select
Selection.ClearFormatting
Next oLink
.Close SaveChanges:=True
End With
strFile = Dir()
Wend
Set wdDoc = Nothing
MsgBox "finished.", vbOKOnly
End Sub
Private Function BrowseForFolder(Optional strTitle As String) As String
'Graham Mayor
'strTitle is the title of the dialog box
Dim fDialog As FileDialog
On Error GoTo Err_Handler
Set fDialog = Application.FileDialog(msoFileDialogFolderPicker)
With fDialog
.Title = strTitle
.AllowMultiSelect = False
.InitialView = msoFileDialogViewList
If .Show <> -1 Then GoTo Err_Handler:
BrowseForFolder = fDialog.SelectedItems.Item(1) & Chr(92)
End With
lbl_Exit:
Exit Function
Err_Handler:
BrowseForFolder = vbNullString
Resume lbl_Exit
End Function