Find the "Tolerance" bar top of the screen and drag it down to 0%. When set to 0%, your paint bucket will only fill in pixels that contain that exact red color. This likely will not change the red in the edges, though. Keep filling in individual pixels or play around with the tolerance meter until you get your desired result. If you do play around with the tolerance meter to fix the edges, you should try drawing a temporary black square (or some color that isn't green/red that you can recolor to green/red later) around the black radio-wave icon so it isn't affected when you fill the edges in at a tolerance other than 0. Be sure to keep your "Flood mode" at contiguous (the light bulb icon).
Note: the "Flood mode" icon (which is probably already set to "contiguous", the light bulb icon) can control whether or not to fill in all of the exact red in the image or just the exact red that touches the area you're filling in. You will probably only need the contiguous option for this task.