The team initially suspects a black-market adoption ring. However, the profile shifts when they realize the killers are a married couple, Robert and Linda Reinman, who lost their own baby, Michael, due to a medical tragedy.
The couple is trying to "replace" their lost son. They keep the male babies that meet their specific criteria and discard the mothers and "imperfect" infants. Why It’s Notable [S5E5] Cradle to Grave
The "interesting story" you're referring to is likely the episode " Cradle to Grave " (Season 5, Episode 5), which is widely considered one of the series' most disturbing and memorable "unsub" (unknown subject) cases. The team initially suspects a black-market adoption ring