Does traditional kidney stone surgery leave a scar?

Possibly: If by "traditional", you mean the need to surgically cut out stones from the kidney, ureter, or bladder then yes. These operations are rare in the western world nowadays, but they can be done via minimally invasive methods to minimize scarring. However, nearly all stones can be managed with external lithotripsy (noninvasive), endoscopically (no scar) or percutaneously (small scar) these days.