Hi Mike,
Not all umbrellas are constructed the same way. Some of the more efficient, better designed silver umbrellas do have silver on the interior of the black backing. Off hand I don't know the make and model of those umbrellas. Most umbrellas with a black removable backing just use a thin black nylon and yes, when there is no silver lining and the umbrella's lining is white, then some light is wasted as it passes through the white material and is absorbed by the black backing as opposed to passing through the white material and hitting the silver interior of the backing, and then some light is returned through the white material.
How much different is it in terms of efficiency? I don't know but I don't think it's anything to be concerned about unless your flash is of very low power and then you probably have more problems that the lining of your umbrella 