恤

Vertical heart radical on the left - the side-form of 心. Anchors 恤 in the emotional-state family alongside 怕, 性, 怀, 慢. Carries the meaning core: showing sympathy or relief is a movement of the heart toward another person's suffering. The 'T-shirt' sense in T恤 is purely a phonetic loan from English 'shirt' and ignores the radical entirely.

Right component supplies the sound: 血 xuè → xù through final-glide loss. Adds a faint semantic match - kinship by blood is the strongest call to sympathy, exactly the original sense of 恤 ('to take pity on a kinsman in distress'). Pictograph of a sacrificial bowl with a dot of blood inside; same shape in 衅.