Originally Posted by Yoshi212

I feel the welcome on a private jet is handled by the crew. The cabin attendant(s) and flight crew tend to welcome the passengers according to their role (pilot makes a brief review of the flight plan. As the jets are smaller the attention is key. A welcome at the door, offer of drinks and relaying any cabin notes such as which seats turn into beds and lav location(s).

If a gift box was offered to me upon boarding I might find it odd or impersonal. Amenity kits similar to those given to premium passengers makes sense but can also be something found in the lav or handed out during service as they're not needed for all services . A departing gift could be a nice way to standout and make the memory go beyond just the flight.