You write a letter to the legal office at Tams-Witmark Music Library (google them for an address) and report what you did here. The theatre will probably only get a slap on the hands for it, but they may have to pay something, because this is illegal.
I reported a theatre once because they were going to do a Neil Simon play with an all-male cast. Well, Neil Simon didn't get rich or become the most commercially successful playwright of the 20th Century by being stupid. The theatre had to cancel that production and replace it with a show they had to do correctly.
Good luck with this.
NYC Visitor and Broadway Fan