If the other airfield didn't tell your customer there would be a charge for the approach when he called them, then they can't levy a fee, as a contract wasn't formed.
I'd check this point with your chap, if only to prevent him repeating the trip in the future!
Understanding the need for goodwill between neighbours, perhaps it would be as well to ring the principle of the other airfield to discuss the charge. If they still want to make a charge, a compromise might be to send them the landing fee only.
Sounds like a bit of sharp practise, but if you explain that your chap wasn't told there would be a charge, they may back straight down.