The enjambment in "Remains" suggests a somewhat halting, disjointed, and even nervous retelling of the story. It also heightens the conversational nature of the poem; the sentences aren't forced into aligning perfectly with the poem's line or even stanza breaks. This mimics natural speech patterns, while, in certain moments, also indicating that the speaker isn't as comfortable talking about this as it might seem.
Line 1 breaks just before the speaker says why these soldiers were "sent out." The enjambment subtly echoes the content here: it's as if the soldiers are "sent out" across the line break, the blank space representing their lack of agency. They are just following orders; if they're sent out, they must go, even if they're not sure why yet.
An even more evocative moment of enjambment comes in the break between stanzas 2 and 3:
... and I swear
I see every round ...
On the one hand, this enjambment creates a sense of building of tension and anticipation: what, the reader wonders, does the speaker "swear"? The white space between the stanzas might also represent the speaker's apprehension about saying the next line—because this is the line that describes, in graphic detail, how the looter died.
There's then another enjambment between stanzas 5 and 6:
But I blink
and he bursts again through the doors of the bank.
The white space here evokes that blink, while the enjambment again makes one stanza spill over into the next; the next line bursts onto the page just as the looter bursts into the speaker's mind.