The white dots on Marble from dropped tools are most likely stun marks. Stun marks can occur when pointed objects impact the marble crushing the crystals and leaving a white mark, dot or line.
For this reason, you should always avoid scooting furniture or dragging anything heavy over marble floors or using marble countertops as a work bench for home projects, etc.
Unfortunately, stun marks are usually permanent. There are a couple repair options, but none are perfect and often look as bad or worse than the original stun mark.