DIAGNOSIS: That's a mechanical grind, not an electronic beep. It typically means something is interfering with the lifting column's internal screw or the gears are dry/binding.
FIX: Isolate which leg is noisy. 1) Clear the desk top and get underneath. 2) Have a helper press the up button while you listen to each leg. Once you've found the noisy one, look for an obvious obstruction. The most common culprit is a cable that got wound around the inner telescoping tube. Untangle any wires running to that leg.
IF THAT DIDN'T WORK: If there's no visible obstruction, the internal lift mechanism likely needs lubrication. Vari specifically recommends a dry PTFE lubricant (not a wet oil or WD-40). Extend the desk fully, and spray the dry lubricant into the seam between the inner and outer tubes of the noisy leg. Work the desk up and down a few times to distribute it.
HEADS UP: A persistent, loud grind from inside the leg can mean a stripped gear. If lubrication doesn't quiet it down within a few cycles, stop using it and contact support. Forcing it can cause complete failure.