disagreement re deposit

Tenancy Types and Management

Hi, I was hoping you could help me, just had a tenant move out on the old deposit scheme and there is an issue re one of the rooms in their flat. All rooms have storage heaters which have caused some localised damage from the dust build up inside which has left black marks. This has happened in all the rooms and we have no issue that it is our responsibility. The problem lies in the living room which was now has soot marks all over the room. They are big rooms and this has not happened in any of the other rooms. We know that they burnt many candles and attribute this excess marking to smoke damage from the candles. They are saying it is from the storage heater. We have had no other such problems with storage heaters in other flats. The tenant never advised us that there was a problem in the 3 years that they rented and are now saying they will claim damage to health from the fumes. We propose to return half the deposit as a gesture of goodwill until the issue is resolved. I would assume that we need to get a sample checked or something but not sure where to go from here - are there companies that can do this and do we have a case for them to repair the damage if it is proved to be candle smoke? Sorry its a bit of an essay would appreciate any help/advice you can give.
Regards