I have a pair of Qi-compatible wireless charging pads, and I've noticed that when a device is charging, the pad will emit a quiet but noticeable squeal in a relatively high frequency range. Perhaps it's because the pads sit on my desk near my bed, that I notice, but I'm curious what might be causing the squeal and if there's anything I can try to mitigate it.
Wireless charging pads work by inductive coupling. In the pad is a coil, and in the device being charged is another coil. When these coils are close together, they have a high mutual inductance, and we can use this mutual inductance to transfer energy between them, as in a transformer.
The trouble is this: an inductor is also an electromagnet. As the current oscillates in the coil, the magnetic forces also oscillate. These magnetic forces act on the individual turns of the coil itself and ferromagnetic materials nearby, causing audible vibration. Magnetostriction can also play a role.
Besides the charging coils themselves, there are probably more inductors in the circuitry that converts the 60 or 50 Hz mains AC to the higher frequency shown here.
I don't know that there's much you can do to mitigate this noise, other than remanufacturing the device. You might try setting the charger on a neoprene or rubber pad, which might at least prevent some of the vibration from coupling into your table. The better solution is usually to move the oscillation frequency above 20 kHz where it can't be heard by humans, or to more solidly support the coils so they can move less.
The following is just a guess because there is not enough information, but I post it as an answer because I had the same effect in wireless charging system that I built.
Some capacitors, ceramic and film in particular, can emit audible noise when operated at (or near) audible frequencies.
While not a big issue, this noise originates in vibrations, which can lead to a mechanical failure on a PCB and have minor electric effects which can be significant in a high precision electronics. These effects are not desirable and are not restricted to audible frequencies.
In your case, the only issue is the annoying sound. You can try to take the charger apart and find the "loudest" capacitors - these can be replaced with better (and usually more expensive) capacitors which emit less noise. See this article for a related discussion.
The other source of audible noise in electronics are transformers, however, since the sound is in high frequency range, it is not probable that any transformer has something to do with it.