Question: If someone calls a tile while someone else picked a tile from the wall and looked at it, since the caller get the tile should they hide the tile in an arbitrary position in the wall?

Answer: To protect the integrity of the game, a tile that is picked from the wall must be put back in the exact position from where it came. You would never arbitrarily place the tile in a different position in the wall even if the tile was seen by a player. This ruling is not in Mah Jongg Made Easy.

Source: National Mah Jongg League Bulletin (2021)