'TH' is 'थे' for me. But you are right even 'THE' is 'थे' which you would expect as 'दे'. So a slight problem there.
But by far the best hindi transliteration tool that is around. It almost keeps in mind the Indian way of spelling and pronouncing hindi words in english. I am more than impressed by it. And remember knowing google, its only gonna get better than this. Maybe these discrepencies will be fixed in coming days. They have an open discussion for getting feedback. the link is on the same page. If you read it you will find other discrepencies like no 'पूर्ण-विराम'. Maybe you can put your discrepancy there. I think the open discussion is to fix these problems.