As asked, what do you mean by legit? Just that the main instructor has the rankings he's claiming in TKD and judo? If so, read below:
His website does not give a whole lot of information, so I'm going to assuming his "certified" rank is in KKW. If so, you could search the kukkiwon registry, but I believe you'd have to ask your instructor for his dan number (different than his rank, an actual number given when he got certified), to confirm. Tagging
@andyjeffries just in case I'm wrong on that.
Regarding his judo rank, there are unfortunately a lot of different judo organizations out there, so without knowing which one he's a part of, it would be tough to state for certain how to verify.
Some instructors will show their certificates on the wall somewhere in the office. If he happens to do that (I'm assuming you're not looking to direct ask him) than you could take a look at those to get the info you need.
Beyond that, are you asking about tkd/judo in general, or if what they're teaching works, or something else?