gtk-window-unstick (window)

window -- a gtk-window widget

Asks to unstick the window, which means that it will appear on only one of the desktops of the user. Note that you should not assume the window is definitely unstuck afterward, because other entities, e.g. the user or window manager, could stick it again. But normally the window will end up stuck. Just do not write code that crashes if not.

You can track stickiness via the "window-state-event" signal on the gtk-widget object.