It is a problem with that small text and your sample might not tell the whole story.
You might get something from
(1) colour select the background with an increased threshold value. Not too much or it eats into the text.
(2) bucket fill the selection with white.
(3) selection off and play with brightness and contrast filter.
One thing you could try to assist the editing, is scale the image up say 400% do the editing then scale (25%) the image back down to original. That should introduce a bit of anti-aliasing to the text and make it less 'pixelly'
You might get something from
(1) colour select the background with an increased threshold value. Not too much or it eats into the text.
(2) bucket fill the selection with white.
(3) selection off and play with brightness and contrast filter.
One thing you could try to assist the editing, is scale the image up say 400% do the editing then scale (25%) the image back down to original. That should introduce a bit of anti-aliasing to the text and make it less 'pixelly'