While they are known for their high-pitched, squeaky vocalizations, these sounds are more like chirps, whistles, and trills. They use these sounds to communicate with each other, not to express any sort of lunar connection.
The myth of animals howling at the moon is often associated with wolves, but even this is more of a cultural trope than a scientific fact. Wolves howl for a variety of reasons, such as territory marking, communication within a pack, or even just because they feel like it.