From the Super Mario Wiki, the Mario encyclopedia
A Toad's Painting is a painting with a Toad trapped inside that appears in the Luigi's Mansion series. The intentions of King Boo and his forces for trapping the Toads varies from game to game, from it being a form of fun, to trapping them out of revenge.
Luigi's Mansion: Dark Moon
Five Toad's Paintings appear in Luigi's Mansion: Dark Moon: a red Toad in Haunted Towers (B-3), a yellow Toad in Old Clockworks (C-5), a blue Toad in Secret Mine (D-1), and a green and purple Toad in Treacherous Mansion (E-2), after they were sent by E. Gadd to look after the mansions. After Luigi frees a Toad using the Dark-Light Device, he then has to bring them to a Pixelator Screen so they can be brought back to E. Gadd's Bunker, thus clearing the mission.
Luigi's Mansion 3
Three Toad's Paintings appear in Luigi's Mansion 3, containing the Toads Luigi invited to The Last Resort: Toad in The Great Stage guarded by Amadeus Wolfgeist, the blue Toad in the Unnatural History Museum guarded by Ug, and the yellow Toad in The Spectral Catch guarded by Captain Fishook. Once Luigi captures the boss and frees the Toad using the Dark-Light Device, he is prompted to bring them to the elevator so they can return to E. Gadd's lab, which is immediately followed by an intermission of Hellen Gravely watching him via security camera.