Why does my patch leave a square of dark sticky stuff around it?

No need to worry, it is most likely just bits of dust and dirt catching in the adhesive that makes the patch stay on your skin. While the patch is in place, there is not too much you can do. Try not to remove the patch or pick at the edges because it can make the patch not stick. Once you take the patch off, try rubbing a little bit of oil on the marks. They should come right off with a little scrubbing.
Still not working? If the sticky stuff bothers you and you want a contraceptive method you do not have to remember every day or every time you have sex, you may want to check out the implant, the IUD, the ring, or the injectable.
Try a different method: implant, IUD, Ring, injectable.