Not many people know this... that trim section is easily removed
Take off the doorcard as usual, then slide a wide narrow blade (gasket scraper type tool) between the join of the trim and doorcard at the top of the doorcard and ease it gently up and up the front of the doorcard. It'll then be easy to pop off the doorcard altogether. You can then clean it thoroughly and snap it back on. I tested it last year as I was going to recover my trim panel in leather - its still on the to do list for me though