The moral I draw from this very ancient tale: If you try to draw sharp lines in a continuous process and you end up looking silly, it's your own darn fault.

Removing grains of sand is a discrete process. The real key is recognizing what is implied by the use of the word 'heap' - so the collection of grains remains a heap until it no longer meets the criteria.

The Ship of Theseus is a much better statement of the problem, as there are enough different meanings of 'identity' that resolving the equivocation between them is a real challenge.