Without the S on this title, you might think the two sections of the poem both relate to the same hurt hawk. That S, plus the specific times mentioned, helps a brother along. This title works like a label, making it easier to get right into the description immediately. The poet is all about accessibility and directness.
The alliteration in the title pairs the two monosyllabic words together in a tight bundle, so they almost become a new idea, the hurt inseparable from the hawk. Somehow it also makes it easier to see these "hurt hawks" both literally and symbolically, that is they are actually hurt birds, but they also will be used to discuss something elemental about what it is to be wounded or unable.