No need to detail strip an 870 for cleaning- in fact, it's a bad idea to try. Some parts are pressed or riveted into place and not meant to be removed save for replacement (and few ever need replacing).
Clean the trigger plate assembly as a unit, immersion into a simple solvent (hot water and dishwashing detergent will do, or spray gun cleaner followed by compressed air and a relube). If you soak it in water, follow up with a good rinse in hot water, drying in a warm place or direct sunlight and re-lubrication.
Unless the gun has been submerged, rained on a lot etc nothing further than field stripping is needed (see the owners manual or Remington's website for fieldstripping instructions). Even if that is the case there is no need to do more than removing the furniture to get full access to all the metal surfaces.
lpl/nc