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Explanation
The Joke
A startup founder gives a tour of his office, explaining the company's business model: "Our startup is called 'Their.' We were originally called 'There' but we made 'Their' a more acceptable term." When asked what the company actually does, he explains: "We continue existing until grammar-obsessed people pay us to stop." In other words, the startup's entire business model is being a grammatical annoyance -- they named themselves "Their" (or previously "There") specifically to irritate grammar pedants, and they monetize that irritation by charging people to make them go away. Once they are paid, "we change our name to something even more annoying and start over." The final panel reveals their ultimate weapon: the word "their" displayed in a way that implies maximum grammatical provocation.
The comic imagines a startup whose entire value proposition is exploiting the obsessive tendencies of grammar pedants. It is essentially a protection racket built on the their/there/they're confusion that drives a certain type of person absolutely crazy.
The Humor
The humor targets two things at once: the absurdity of startup culture (where almost anything can be pitched as a viable business model) and the intensity of grammar pedantry. The joke recognizes that some people are so bothered by their/there/they're confusion that they might genuinely pay money to make it stop -- which is both a commentary on internet grammar culture and a parody of the "move fast and break things" startup ethos. The final panel punchline, simply displaying "their" as though it were a weapon of mass destruction, perfectly captures how something so trivial can feel so maddening to the right audience.