I don't know why they don't change the TUN service to LHR. Tunisian traveller could then benefit from good transfers to Montreal and New York as well as other points in the UK and Scandinavia. I know a lot of friends who choose to go through CDG with AF because changing of airports between LGW and LHR is a nightmare.
I don't think that GT are that interested in passengers who are connecting to BA's LHR transatlantic services, I think they are after more business class passengers on their aircraft. The flight from GIB-LHR lands at 2200 hrs, so the passengers would have to stay overnight in a hotel.
I don't know why they don't change the TUN service to LHR
Because sadly with only 2 runways and every airline wanting slots not every destination can be served from Heathrow. You could argue that people from every Gatwick destination could benefit from connections.