Hi cassa, I work in an office that deals with reports of anti social behaviour, we work closely with the police, social services and environmental health, amongst other agencies. If your tenant's neighbour has any concerns she should contact the relevant authority, who will ask her to complete incident diaries and would consider installing noise monitoring equipment, etc.
Sadly, we get a lot of complaints from people who simply want "nice" neighbours, i.e. not neighbours whose rent is paid by HB. We often get the same when an Asian or African family moves in. I would suggest you advise the old lady to contact her local authority / council who will point her in the right direction, you have been more than helpful already in responding to her and speaking with your tenant.
However, replacing the front door does sound fairly suspicious, although her excuse may well be valid, I would keep an extra close eye on it.
Hope everything works out x