Mortimer is her brother. As stated in the plot summary on Wikipedia:
While murdering the family of the man who captured him, Indio carries a musical pocketwatch that was a memento of his youth, using it to time the duel. Flashbacks reveal that he had taken the watch from a young woman (Rosemary Dexter), who had shot herself as he was raping her after having murdered her husband. The incident has haunted Indio, and he smokes an addictive drug to cloud his memory.
Mortimer takes Indio's watch and Manco remarks on Mortimer's resemblance to the woman in the photographs. Mortimer reveals himself as her brother
According to IMDb, this is the dialogue:
[Mortimer has just recovered the watch from Indio, which contains a
picture of the woman that Indio raped]
Monco: [peers at the picture] There seems to be a family resemblance.
[He hands Mortimer the similar watch with the same picture he had
Col. Douglas Mortimer: [pause, then] Naturally, between brother and
According to Howard Hughes's Once Upon a Time in the Italian West: The Filmgoers’ Guide to Spaghetti Westerns:
After Indio’s death, the dialogue between Mortimer and Manco explains the revenge motive, reinforced by Morricone’s subtle underscoring. Manco looks at the picture in the watch and notes a family resemblance. ‘Naturally,’ answers Mortimer, ‘Between brother and sister.’ Manco says that they have become rich, but for Mortimer revenge is enough. Mortimer listens to the chimes, while Morricone’s ‘Goodbye Colonel’ accompanies the scene, again incorporating the carillon, but now with lush strings and chorus. His sister avenged, Mortimer is content and rides into the sunset.