The image above is from the first walk sequence. This demonstrates that the object was by her left side early on in the filming.
The image above is a bit harder to see but I believe that the object is visible at the lower extremity of the arm on the left side.
Perhaps this might explain why she would have a chunk of hair in her left hand in frame 352 above.
I will be carefully scrutinizing the film to see how many times this object can be seen.