You'd need to use PHP and load a GroupTable object then you can adjust its params using PHP. Example as follows.
Code:
$group = new \CB\Plugin\GroupJive\Table\GroupTable();
$group->load( GROUP_ID_HERE );
if ( ! $group->getInt( 'id', 0 ) ) {
return;
}
$group->params()->set( 'gj_custom', 'NEW_VALUE_HERE' );
$group->set( 'params', $row->params()->asJson() );
$group->store();
If you're familiar with JSON MySQL functions though you could do this directly against the database as well I suppose. Custom parameters are stored in the params column.