The plastic mesh is a good way to reduce the frequency of aluminum screen injuries, as noted by Joshua. As many solutions often create problems of their own, hopefully lesser problems, one thing to keep in mind when going to a plastic mesh, such as in the above solution, is the size of the mesh holes relative to the chameleon's head, neck, etc. If the holes are close enough for the chameleon to try to push through them, it will try. Most chameleon heads are streamlined so that it is easier to push through than it is to reverse back out, especially if a tight fit. When the hole size is just right, chameleons will get stuck. In the short run it will rub a raw spot on the top of the neck, as the chameleon will struggle. If not noticed soon enough, the chameleon can die there. While we often attribute above average reptile intelligence to chameleons, squeezing through holes "because they are there" is not an area where they excel intellectually. If it happens, the easiest and safest way to extricate the animal is usually to cut the mesh carefully with scissors, sliding them between the mesh and the chameleon, keeping the cutting edge and tip off the chameleon's skin. It can be done relatively easily.
In the photos provided, the mesh holes are plenty small enough to not be a problem with the chameleon pictured. For others considering such, try to be sure the holes are either safely too small, or safely too large, for there to be any risk.