This method works as well and avoids the need to delete faces:
I uploaded a Step file so you can preview the results.
Select the two faces and knit them together.
Actually, You can skip this step , and use the Offset command on these faces instead. I'm not sure why I always knit before I offset... Maybe a really old version required it?
Select the new surface and offset it by the depth you want the cut to be (1.5mm)
Cut - Extrude your door profile up to the offset surface
The end result looks much cleaner at the intersection of the various faces.
You don't need to do this, but another option is editing your original sketch and extruding it as a thin feature (up to surface like the above method). I think offsetting the sketch like you did is the better option. Just keep this method in mind for future use if you need it.