[charliebub]

Hi, I received mine today too. I don't have this problem though - the pen will write right up to (and even along - using the screen-edge as a sort of ruler) the black plastic edge.
This is true for both beginning the stroke, ending the stroke and part-way through the stroke.

p.s.
This is true for all angles of the pen, not just perpendicular. Held as in your image my pen writes perfectly - so-far!