They must realize that they finally have a President that is irrational enough to take them seriously.
Trump has shown himself to be a conspiracy theorist (Obama birth certificate, JFK assassination, climate change denial, anti-vaccinations), so this petition was likely created because they think he'd be open to the idea that the moon landings were faked.
At the end of the day, it doesn't matter who is the Prez. Facts are facts are facts.
Worst case scenario, though, is that someone convinces Trump he'll go down in history as the person who Exposed the Truth (as he wanted to do with Obama's birth). He'll drag in the NASA heads, and demand that they reveal all the evidence that proves it was a hoax. When they tell him, truthfully, it doesn't exist, he'll explode and decide that, as his science head tells him, we don't really need publicly funded research. After all, they wouldn't play ball with him, and Trump doesn't lose gracefully.
Fortunately, Trump is big on American exceptionalism, and I suspect he'd not be big on taking away one of the U.S.'s biggest scientific bragging points. Because he's all about the bragging points.