OK, just had to keep plugging away at it. The following worked, displaying the image and linking it to the geocaching profile. Your examples over at UBBDev were most helpful.
Code
<?php
$export_tags = array (
  0 => 
  array (
    'tag' => 'GeoStat',
    'descrip' => 'Geocaching Stats',
    'prompt' => 'Your Geocaching.com uid, like xxxxxx-xxxx-xxxx-xxxx-xxxxx',
    'regex' => '([a-f0-9-]+)',
    'markup' => '<a href=\\"http://www.geocaching.com/profile/?guid=\\\\1"><img src=\\"http://img.geocaching.com/stats/img.aspx?txt=View+my+profile&uid=\\\\1">',
  ),
);
?>