That is what I do as well. They will figure it out eventually I bet in one part of town, and then within days, somehow, they will all know how to pull them out.
I watched a demo of how the 'green' bin recycling works. It's kind of gross, but kind of smart.
What they do is put all the green bin stuff into a big tank, and then fill up the tank with water to make a green bin slurry. Then it is kind of ground up with big rollers or something, and the plastic is scooped out, the slurry goes into a big tank / silo thing, and the water is evaporated with a big fan (this is why the residents who live close to the facility complain about the bad smells) and eventually it ends up as dry compost material.
The city uses baby diapers put into the compost as the last layer in the garbage hill!
What is interesting is the diversity between cities in terms of acceptable green bin materials.
Most other cities won't accept diapers.