Will the James Webb Telescope be able to see the lunar landing sites?

Unfortunately not, but not because it wouldn't have the resolution. This is a very cold telescope. It sits at this point called Lagrange point 2, which is roughly 4 times the distance of the moon from earth, and the moon is a very warm object for an infrared telescope. So, in fact, we've designed this big sun shade, which is the size of a tennis court, precisely to block out the heat of the sun, the Earth, and the moon. So we can never look back at the Earth, the moon, and certainly not the sun. And so, unfortunately, the moon will remain inaccessible to us...