That piece of trim is easy to remove. It is held in by a few metal posts, as indicated in the above post. They are simply pressed into plastic retaining holders, or whatever, by friction. Gently pry up along the length a little at a time. You'll feel it coming up. IIRC, the part you show is where the trim sort of seats in under the black plastic. The black plastic and door handle portion does not move. I have removed those door pieces many times and not had the problem you're showing. I am hoping just removing and installing will fix that gap.

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