The phrase "infinite mercy" means having boundless and never-ending kindness and compassion towards others. It suggests showing endless forgiveness and understanding, even in situations where punishment or anger might be expected.
The memorial service is then followed by the celebration of a «Mass of Entrustment,» in which each retreatant is invited to reconsecrate herself body and soul to Christ and to entrust herself and her beloved children to the Infinite Mercy of Jesus. (faith.org.uk)
Redeemed by His infinite mercy, His child, and forever, I am. (redeeminggod.com)