That's quite a lot of people you are going to have to warn!
Consider that the moon's orbit is tipped at 17° to the equatoral plane. The rope will tend to wind its way North or South (depending on the orientation of the orbit at the time.) Once it gets to about 17° of the pole,(Actually less, sometime before that, the tension on the rope will be greater than the friciton between the rope and the Earth.) then it will just keep slipping off. Then, as the month progresses, the moon's position will change orientation to the Earth's axial tilt. As it does so, and the Moon gets closer to the equatorial plane, the rope will work its way closer to the pole again. After the Moon crosses the equatorial plane, the rope will start to work its way back toward the equator and then eventually to the other pole. Then the process repeats in the other direction. After a while the Earth will look like a giant ball of string, with just the ice caps exposed.
The above is even a over simplfied scenerio as it ignores the torque placed on the Earth by the off center force of the rope as it works it way toward the poles.