Very interesting question! Why are the solder balls there in the first place and where did they come from? Are they from the wave soldering operation where the solder splashed and the solder stuck to an uncured solder mask? Are they there from a solder paste that did not reflow and was no longer solderable? Are they there because the pads were incorrectly designed and the solder balls are beneath the chip components?
These must be defined first so the proper method of prevention can be implemented into the process.
Now if you cannot define why they are there, then according to IPC-A-610, page 5-14, Acceptable Class 1, 2, 3 - solder balls are entrapped/encapsulated and do not violate minimum electrical clearance, with an added Note: Entrapped/encapsulated/attached is intended to mean that normal service environment of the product will not cause a solder ball to become dislodged.
Therefore if they violate any of these requirements they are a cause for rejection and are identified as a defective condition.
Now how can they be removed?
One must determine what is keeping them in place, if it is flux, then the flux must be removed and the solder balls will also be removed with the flushing action of the flux removal operation.
If no clean flux is used and there is no cleaning process, then we have an issue. If they are stuck to soldermask then we also have an issue.
The best way I found was to use a bristle brush and rub them off them try to flush them off with an air knife or air nozzle. Trying to use the air nozzle by itself may not be powerful enough to dislodge the entrapped solder balls.
Hence establish your process to minimize the formation of solder balls by proper process controls in both the solder paste and the reflow profile.