This cartoon seems to be a direct commentary on the story, namely, Little Red's surprising inability to distinguish her grandmother from a wild animal. This is one of the things that Thurber commented on, noting that someone's grandmother doesn't really look like a wolf at all. This strikes me as a very good point, and one of the major things that pulls me out of the story. To an extent, for fairy tales, the reader suspends disbelief about things that don't quite make sense. There are times that I believe the tale can go too far in its disregard for logic, and this moment might be one of them. If we go with Perrault's interpretation that the wolf is a man, it still doesn't exactly make sense, though it almost becomes a point that is being made. The little girl is apparently foolish enough as to not be able to distinguish the rapacious gentleman from a close family member.
I find this cartoon to be amusing, if you look at the story from the grandmother's perspective. Especially if the grandmother is assumed to have survived being eaten, as in Little Red Cap, she then has to listen to her granddaughter essentially saying that she looks like a wild animal. That's just absurd enough to be funny.
Also, it raised an interesting point in my mind that the story is often not examined from the grandmother's perspective. Symbolism aside, if the grandmother is just a grandmother, she definitely gets the short end of the stick in all the versions of the story. In some, she seems to have some of the same problems as her granddaughter, easily believing that the wolf's voice is that of her granddaughter and allowing him entrance. Regardless, the grandmother definitely was eaten by a wolf, and then had her granddaughter mistake the wolf for her, and didn't even get any of the goodies that Little Red was bringing her. We should all take a moment to pity the grandmother.