The passenger stairs will go away when you select the departure/pushback option.
If they don't in your system, please indicate a reproducible case indicating the airport and the airplane used. Possibly, use a default airplane with the default configuration that comes with GSX and on a default or an FSDT scenery. If the problem doesn't happen with an all default situation, it might be possibly related to the airport, so please indicate where this happens, the airport, the gate and the airplane used.