Mollify
Etymology
From Latin mollificare, "to make soft," from mollis, "soft," plus facere, "to make." The literal sense of softening a hard substance carried over to softening a hardened mood; to mollify someone is to take the stiffness of anger out of them.
verb · /MOL-ih-fy/
To soothe the anger or hurt feelings of someone.
What it names
The word for softening a person who is upset — calming their temper enough that they’ll listen or let a grievance drop.
Example
A quick apology and a full refund mollified the customer before the complaint reached the manager.
Related idea
Placate focuses on stopping someone’s anger, sometimes with a concession; to mollify emphasizes gentling the feeling itself.