How to make things opaque using GIMP?

• Fuzzy select the background with the default threshold. Shift-click inside closed areas ('a','e','o') to add them to the selection. In your very specific case (only two constrasting colors in the image), you also do a color selection and use the background color (so yo udon't have to worry about closed areas)

• Select>Grow by one pixel so that the selection extends over the pixels on the edges of the letters (if the image is dirty (JPEG artifacts), you can grow by 2 or 3px)

• Colors>Color to alpha and remove the background color. With the selection above, C2A will only apply to edge pixels and leave the core of the letters untouched.

Color to alpha has affected also partially in the middle of the letters. I guess you have tried to get rid of the remnants of the green color with the treshold sliders in Color to Alpha dialog. After removing the background you have partially transparent letters like these:

How to fix:

GIMP has the curves adjustment as well for RGB channels as for Alpha. Apply Colors > Curves > Alpha and adjust the curve. The right adjustment makes the letters visually opaque, saves the partial transparency of the edges (=anti-aliasing) and it doesn't lift up background:

In my case making the curve steeper did the job. You may need a little S-shaped curve to keep the background invisible.