Untrimmed surface edges are defined by the control points along the edges. Rebuilding with fewer control points for the surface reduces the number of control points defining the surface edges and therefore usually changes the shape of the edges. Rebuilding with more control points usually results in different locations for the control points which may change the shape of the edges.
I don’t know if this helps, since rebuilding can be used for so many different needs, but if you’re looking to reduce the amount of control points so that you can globally control point edit the shape of a surface, you might want to try SoftEditSrf. It has a FixEdges option and you can change the influence in U and V of the area you’re editing.