Triangle to Quad produces disconnected triangles Using the Triangle To Quad option on this mesh produces a bunch of disconnected triangles, like in the photo.



What is the easiest way to remove these so that they are replaced by quads?
From that exact view (all those exact faces selected): 


Hit X, then faces to delete the mess you have.
In edge mode,Alt+Right Click an edge, to select the loop around the hole.
Hit F to fill with an ngon.
Then hit Ctrl+T to Triangulate. 
Then hit Alt+J to do a Triangle to Quad


EDIT: 

Mr Zak's suggestion to use Grid Fill greatly improves this answer by reducing the last three steps to just one:


Hit X, then faces to delete the mess you have.
In edge mode,Alt+Right Click an edge, to select the loop around the hole.
Hit Ctrl+F then Grid Fill