私のSQLは確認が必要かもしれませんが、招待者自身を招待した場合に付与されないように、バッジクエリにこの行を追加できると思います - AND i.invited_by_id <> u2.id
例えば、以下のようになります。
SELECT u.id user_id, current_timestamp granted_at
FROM users u
WHERE u.id IN (
SELECT invited_by_id
FROM invites i
JOIN invited_users iu ON iu.invite_id = i.id
JOIN users u2 ON u2.id = iu.user_id
WHERE i.deleted_at IS NULL
AND i.invited_by_id <> u2.id
AND u2.active
AND u2.trust_level >= 0
AND u2.silenced_till IS NULL
GROUP BY invited_by_id
HAVING COUNT(*) >= 1
) AND u.active AND u.silenced_till IS NULL AND u.id > 0 AND
(:backfill OR u.id IN (:user_ids) )