They are not interchangeable. Relinquished in the general sense means to stop doing something in this context. Relented means to quit something that a person changed a long-sanding position. His Dad relinquished his Monday objection and let John use the family car. His DAd had never allowed John to use the family car, even though JOhn had been licensed for two years; but he relented for the Prom and handled the keys to John.