No, a variable that causes Earth's oceans to dry up or recede deep underground would not directly affect the orbit of the Earth and its moon around each other. The gravitational interaction between the Earth and the moon primarily depends on their masses, distances, and the laws of gravity.
The presence or absence of water in Earth's oceans does not significantly affect the gravitational attraction between the Earth and the moon. The gravitational force between two objects depends on their masses and the distance between their centers of mass. While the mass distribution on Earth may change slightly if the oceans were to dry up, the overall mass of the planet remains nearly the same. Therefore, the gravitational pull between Earth and the moon remains largely unaffected.
It's important to note that changes in Earth's mass or mass distribution on a significant scale could potentially have some indirect effects on the orbit of the moon. However, the drying up or receding of Earth's oceans alone would not cause such significant changes.
It's also worth mentioning that the Earth-moon system is a complex dynamical system influenced by various factors, including the gravitational interactions with other celestial bodies and the conservation of angular momentum. However, the specific scenario you described regarding the oceans would not be a primary factor in altering the Earth-moon orbit.