Nice gift of wood ya got there! If the bark is really thin then just leave it on. If it's rotting and falling off then pull off the loose pieces but don't put too much effort into removing what won't come off easily.
I agree,apple branch trimmings are usualy not thick barked etc.I have used a whittling knife or draw knife for removing bark on pecan branch trimmings etc. -to remove mold or moss on bark..As you mentioned in post- important to have it all dry and sized for fuel load needed, before any smoke.