A gruel-stick is a stick that women carry around during the festival of the full-moon gruel. On this day, a bowl of gruel is presented to the Emperor. The women carry the gruel-sticks all day and use them to playfully hit other people. Shonagon describes this as very flirtatious, although she says that when women get hit with gruel-sticks, they often act like they're angry or hurt.
The Pillow Book of Sei Shionagon