When you say they don't move, do you mean the same spot stays in the same place or that they always are found on the driftwood? If it is the same spot staying in the same place, I would rule out eggs. They should hatch or fall off in less than several months. Have you tried plucking one off to tell us if it has a hard shell?
Regardless what they are, I would go for a bleach water soak. A small amount of cheap bleach(1/2 cup?? ) and soaking at least overnight, will let the chlorine work it's way into any hard shell and kill whatever it is inside. After that it will be easier to remove. That is all based on not being new eggs being laid. After the soak, rinse it, let it dry totally and it will be a fresh start. If it is a fungus or mold, the bleach will likely have changed the setup and the same should not return.