Here are 2 approaches:
1. Test 2 polyline's intersection points (you should find 2 intersection points in this case); then use Curve.GetSplitCurves() to split the 2 polylines (i.e. the rectangle polyline would be split into 2 parts, while the pass-through polyline would be split into 3 parts.; then use Entity.JoinEntity() to merge the middle part of the pass-through polyline with either half of the rectangle polyline.
2. if you can obtain a point inside the green area (any point your code can identify that is inside the area; or simply ask user to pick anywhere inside), then call Editor.TraceBoundary(). This would be similar as running "BOUNDARY" command.