The rio, now filled, takes its name from the existence of a hospice for Catecumeni, that is, Turks, Jews or anyway foreigners, subject to Venice, who wanted to approach the Christian faith in order to be admitted to the social and working life of the city.
Since over the centuries, especially after the battles of Curzolari and Lepanto in 1571, their numbers increased significantly, the hospice was gradually enlarged and flanked by a church, until it assumed its present form in about 1730 by the architect Giorgio Massari.
The Rio Terà now comes alive during the celebration of the Madonna della Salute (Church next to this site) with various stalls selling candies, balloons and cakes.
The filling of the Rio Terà and the adjacent Rio ai Saloni is commemorated by a plaque placed on site.

The front entrance of the old hospice is interesting

and in front, almost hidden inside a small courtyard, is the image of a Virgin and Child

Along the Rio Terà can also be found a sacred image and some coats of arms: