Assuage
Etymology
From Old French assouagier, from Vulgar Latin assuaviare, from Latin ad- ("to") plus suavis, "sweet, agreeable." The underlying image is of sweetening — making something harsh more pleasant. From there it came to mean soothing or softening a distress, as if adding sweetness to bitterness.
verb · /uh-SWAYJ/
To ease or lessen a painful feeling such as grief, guilt, or fear.
What it names
The precise verb for taking the edge off an inner pain — not curing it, but making it bearable.
Example
Nothing could fully assuage her guilt, but the letter of thanks helped.
Related idea
Alleviate applies broadly to any burden or symptom; assuage is best for emotional pain — grief, anxiety, remorse.