According to tradition the Perdon (forgiveness) name dates from the year 1177. That year Pope Alexander III, fleeing from the persecution of Barbarossa, rested in the adjacent Sotoportico (underpass) della Madonna, and promised perpetual indulgence to anyone who recited there an Our Father or a Hail Mary.
All this is supposed to witnessed by the presence of a wooden plaque at the entrance of the underpass,

however, while the presence of Pope Alexander III in Venice seems established, the story seems more a popular myth rather than a historical truth. In the alley you can see in a capital Istrian stone, bearing the monogram of St. Augustine (IHS) and representing a Virgin with Child 

and another one is visible inside Sotoportego della Madonna, representing the Assumption, with the presence of a statue of Pope Innocenzo III.

Entering the Campiello Cà Bernardi, accessed from the small street that starts in front of the capital, in the Calle del Perdon, you can see a classical wellhead in the garden of one of the houses nearby: 

Finally, notice that to access the Calle del Perdon, you crossed the Bridge of Meloni, now a sort of catwalk without steps, which in the past was a real bridge, then modified, preventing the passage for boats