I'm having the same problem since day 1, and it's not related to pressing any key because the frequency is changed when I'm asked to release the parking brake during P/B. Anyway it isn't something that occurs every time I ask for P/B, it's like 60% of the times is happening and 40% not...
The issue in this thread is selecting a GSX menu option using the keyboard, which the way the sim works, cannot be prevented, but at least it can be fixed by using the mouse instead. Yours is completely different, but I can't see how GSX could cause that, since it's not sending any key command when pushback starts, unless you are referring when GSX is asking for a Left/Right direction, in that case it's the same, pressing 1 or 2 when the menu is displayed, will be transmitted to the simulator as well, but it won't if you use the mouse to choose the direction.