Track the motion of the x’s, then attach new layers which just have the texture of the paper. You can clone the texture in AE or Photoshop, easily, since the paper has such a uniform texture.
Heck, you may not even need to track to the motion, if there isn’t much. You could animate the layers by hand to match the movement.
And actually, since there’s so much space around the x’s, you could make the clone layers large enough that they cover any movement.
You could also just duplicate the main layer, draw a mask set to subtract around each x, and offset the layer below until you have blank paper showing underneath.
Lots of ways to do it.