Until recently, a first-time shoplifter caught in any of about 2,000 Wal-Mart stores got a choice: pay hundreds of dollars, complete an education program and all will be forgiven—or don’t and potentially face prosecution.

Corrective Education Co. and Turning Point Justice, Utah-based companies that provide the programs, emerged in recent years as alternatives to the often-overtaxed criminal justice system. They spare law-enforcement resources and hold offenders accountable without leaving the scar of a criminal conviction,...