OK, I'm late but just for the record... The proper way to remove a uniform background (no jagged edges, no faint remnants) is this:
- Add alpha channel if not there: Layer/Transparency/Add Alpha channel
- Select the background with the Magic wand (if you have letters or other holes", shift-click on them t add them to the selection)
- "Select/Grow" the selection by one pixel (so that the selection includes the border pixels of the subject
- Colors/Color to alpha, using the background color (you can also bucket fill in "Color erase" mode, this is equivalent)

The explanation of the "magic" is there.