If it is truly a "coil whine" and not something else (case resonance, fan bearing whine, high pitched noise from the speakers, etc.), then you can't fix it.
The noise is caused by one of the many inductors in the various power supplies (DC-DC converters) used in the machine mechanically vibrating at an audible frequency due to magnetostriction. This happens because of the power converter running at too low frequency - or hitting some kind of mechanical resonance mode that amplifies the otherwise inaudible noise. BTW, even ceramic capacitors can whine due to piezoelectric effect.
In a desktop machine you could replace the offending part (GPU, power supply, motherboard, etc.) for a different model but in a laptop you don't have choice as everything is soldered into the motherboard.
Even desoldering the offending inductor and replacing it usually won't solve the problem because it is due to the circuit design/properties themselves and not the inductor itself. So a new one will have the same issue - the whining inductor isn't defective!
I wouldn't recommend adding any sort of sound dampening because in a laptop this is very likely to compromise the already poor cooling. You will likely only make the otherwise benign (albeit annoying if you can hear it) problem into a very expensive to fix failure due to something overheating.
If you have a laptop with this issue and the noise bothers you, then replacing the laptop is your only realistic option, really. Or wait until you get older and will naturally lose the ability to hear higher frequencies (past 40 years of age you will be hard pressed to hear anything above 15kHz anymore ...).
Either way, before attempting any sort of remediation, do make sure the noise is actually a "coil whine" and not e.g. the speakers emitting it because of some unused mixer input that is set to high gain and is picking up and amplifying internal machine noise.
And yeah, good luck with trying to return a machine for this reason - the computer is not defective, this is a normal behavior (in the sense it works as designed). So it is unlikely the seller will recognize it as a warranty issue of any sort.