The spelling of /g/ is <g> or <gg>. The /ð/ sound is spelled <th> throughout.
This is a contrast between a stop and a fricative, both voiced but well separated in the mouth. It does not cause any problems.
Interesting pairs include:
mugger mother
smugger (meaning more smug) smother
Since /ð/ is a rare sound, the figure for the mean density is very low at 0.6%. The set makes 17 semantic contrasts, giving a high loading of 85% since many of the /ð/ words are function words which do not inflect.
Bergen burthen digger dither diggers dithers Gael they'll gale they'll GATT that gave they've gay they ghee thee go though goes those guy thy laager lather laagers lathers Largs laths mugger mother muggers mothers smugger smother Whig with wig with
John Higgins, Shaftesbury, September 2010.