its good stuff mate, i suggest you leave in all bits of bark hay etc where they are as im sure it all plays a part in adding nutrients, airation etc to your medium.
im sure there is other threads in a similar vein to this one, search through this forum if you aint done so already and the more experienced gardeners out there explain the point of such material being in the compost.
im no grow expert mate but the compost your using won the what compost trials of 2008 and myself and a few friends have used it for our last few grows with great results.
ATB desmo