Symbolism, Imagery, Allegory
When Gratuity's mom claims she's been abducted by aliens and given some super-special mole with a mole gun, her daughter can't help but ask questions:
"But… why?" I asked. "Why would a race of… of intelligent beings travel across the galaxy just to give people moles?" (2.23)
We think this is a solid question. After all, it's not like the mole itself proves anything—anyone can grow a mole on her neck. And as for aliens, well, they're not exactly par for the course at this point in Gratuity's life.
Here's the thing, though: The mole turns out to be part of the Boov's top-secret plan to take over the world, Pinky and the Brain style. Not only does the mole allow the Boov to hear what's going on in the world, it also gives Gratuity's mom commands.
Even though the mole is literally part of the Boov's plan, it also becomes symbolic. For Gratuity, the mole is just another thing that her mom won't be responsible about—she urges her mom to get it checked, but her mom doesn't listen, and Gratuity feels like that's always the way things go with her mom. Yet in the end, her mom is right. So the mole is also a symbol of the fact that Gratuity still has a thing or two to learn from her old mom.
On the level of the book as a whole, the mole is a symbol for the Boov and their, shall we say relocation, to our planet. They take control of Tip's mom's body just as they take control over all human bodies, shuttling them to Florida and then Arizona. The mole, then, is a sign of what's to come.