Looks like the surface finish the maker put on has started to wear off. This is normal and this finish is really only intended to hold the strop in makers condition till it's sold. It has no bearing on the strop quality or ability.
Condition it with some saddle soap mixed to a very thick lather and leave till dry, then buff with the palm of your hand till smooth. You can use the pumice method as described before to get the same texture over the whole strop. This will remove the makers coating and smooth out the surface to a uniform texture. Because it is a Russian style leather, I would recommend you don't use oils on it but soap alone for conditioning. This is only my preference as I have found the soap produces a good draw and lubricant stopping the course nap being lifted.
PuFF