After a little more digging, I came up with this...

BoxObject oBox;

oBox = oMyReport.Section6.ReportObjects("Box3") as BoxObject;
oBox.Border.BorderColor = Color.FromArgb(255,255,255);

And that seems to work. [I couldn't find the 'suppress' property, so I just made the border color white to suppress, and that seems to work].

Kevin