Unless I’m misunderstanding, this has nothing to do with G4P. This is true of all text (and all antialiased images, which characters are) in Processing.
If you don’t clear the background, then anything with a soft edge will compound over multiple frame draws, blooming out and developing crackly edges.
Both @Chrisir and @jeremydouglass are correct in that G4P expects the use of background() inside the draw() method and that repeated antialiasing will blur soft edges.
For G4P there is a possible solution but it might not give you the visual appearance you are looking for. If you have a G4P control then you can make its background opaque with control.setOpaque(true)
This will work for all visible G4P controls. The reason for this is that all visual G4P controls use an offsreen buffer for its graphics, this buffer normally has a transparent background but using the statement above the buffer background is a solid colour. The buffer is copied to the screen every frame overwriting the previous one.