it sounds like the action channel is too deep and the piece of wood was put in there to shim it so the action would cycle properly.
There is no small piece of wood dropped in the stock somewhere as part of the original assembly as far as I know, and perhaps you should consider an other approach like either fastening the shim with epoxy, or better yet bedding it. You will need to know where the issue is first so you can set it to the right height when you bed it.
Perhaps try removing the shim and then slowly tightening the fore stock until there is interference, then back it off a bit. If it does have a piece of wood as a shim it would create uneven pressure on the action and/or barrel, which will likely effect the accuracy to some degree.
Though this is my guess, it could be something else. Have a search in CGN in the gun smithing section for bedding an action.