Hi QweenOfBees,
Are the three items now combined together as one item in your inventory, or is the thread still separate?
Be sure to examine the top mantel (above eye level) of the fireplace before you do anything, see if Sylvie says anything about the tiles.
Then combine the napkin with the bough. Then to that, add the thread. You'll then have a bough with tied napkin in your inventory and should be able to clean the dirty middle tile. Check that you're using the bough in the correct place here.