Their letter refers to a Permit Parking Bay, but there are no marked bays. There is a large area of what one could call "driveway" up against the houses, clearly delimited from the footway.
This sign as one drives in, states it is a parking permit area on the days and between the times on the sign.
https://maps.app.goo.gl/3xs8k9bWqzvuqDHt9However this sign is for use for carriageway parking. What we need to see is where the vehicle was parked, or the CEO photos, (if any). Please note that if any part of the vehicle was intruding into the carriageway then a PCN would have been correctly served.
Forum experience is that there is always trouble in such locations where there is no kerbstone line indicating clearly what is carriageway, footway, and driveway, and what is not. Being in London parking off-carriageway on footway or verges is also an offence, and has been since the 70s, but the PCN isn't for that.