Newer irons have a "clean" cycle which is basically heating up the iron to its hottest and then holding the iron over a sink while you press the burst of steam button. This is supposed to force out any dirt sediment in the iron. If you don't have a "burst of steam", in the past when I didn't have the burst function and saw any sediment come out of the iron I would heat the iron to it's hottest and iron a scrape to help release that dirt.
I think you can wash what you have with only a few threads to trim. You might want to stay-stitch around the edge first.