I think the dropping of the handkerchief - the physical separation of it from David's hand - emphasizes the fact that this is a real, physical thing, brought in by Laura, who, we are given to understand, was not a physical presence in David's room. It seems that now that the picture is gone, she can access David - probably just by staring into the fire the way she was doing when Elizabeth knocked on her door. But Laura's handkerchief didn't leave David's presence when Laura did. Maybe, if I think about this long enough, I'll get an idea as to how it could be that Laura's locket was in the fire in Phoenix and was also there at the cottage for her to show to Vicky.
During the next episode, I realized the significance of the handkerchief, but I think Laura was physically present. Maybe the handerchief is evidence of that, and of course it's there to make ECS take David seriously, and not assume it was a dream.
Good idea, about the portrait having kept Laura out until now.
[spoiler]I think that in Phoenix, Laura duplicated herself, burning her old self and moving on. I doubt that the new Laura appeared sans clothing, since this is the supernatural, not a SF story about cloning or something... so if clothing can be duplicated, so can a locket.[/spoiler]