There are several synonyms for the phrase "pay damages" that can be used in legal or formal contexts. One commonly used synonym is "compensate for losses," which refers to the act of reimbursing someone for any financial or personal losses they may have suffered due to negligence or wrongdoing. Another synonym is "restitute," which refers to making amends or restoring something to its original condition. Additionally, the phrase "make reparations" can also be used to refer to paying damages, as it means to make up for a wrongdoing or injury caused to someone else. Overall, these synonyms emphasize the importance of accountability and responsibility for actions that cause harm or damage to others.