Your story seems... a little impersonal. On the one hand you've got the first person to ever defeat Triela in had-to-hand combat. That defeat forced her to question her purpose, and to reevaluate her fighting effectiveness. Because of her loss, Triela committed herself to seriously learning how to fight, going from an unskilled brawler with too-high expectations of herself to a disciplined warrior with a proper combat mindset. Pinocchio's death caused Triela to think of someone she killed as a person, someone with hopes and fears, goals and dreams, just like her.
Triela didn't have the same impact on Pinocchio, but this girl attacked him and one of his friends, took his pendant, invaded his home and tried to arrest (or kill, for all he may know) his adopted father. She certainly must have seemed strange, with her young age and inhuman strength and speed. If I had to guess, I would say that his short conversation with Triela during their fight made him realize that his enemies had motivations and obligations just like he did.
If Triela and Pinocchio were to meet after their fight with eachother there would be intense emotions for both of them. Not necessarily negative or hostile emotions, and not necessarily expressed, but present nonetheless. Here, I see them talking, but I don't truly see them feeling.

More new ground's being paved here, Tommy, which is something a trailblazer like me whole-heartedly approves of - this is only the second fanfic in the entire section to be based on wallpaper (Sheo's 'Admissions' being first). That being said, your fic could not be more different from the aforementioned mischievous Claes/Triela romp. Nitpickers might question the reasons behind Pinocchio's mysterious and unexpected reappearance in the story, but in truth, whether Pino is a ghost or an actual, physical survivor of his duel with Triela is immaterial - readers should suspend disbelief and lose themselves in the narrative's entrancing aura of sad serenity. Packed with vivid imagery, poignant dialogue and bittersweet moments galore, this composition flawlessly melds all these elements to produce a hauntingly beautiful work that, like Triela's image on Pino's mind, remains indelibly etched on my memory long after I finished reading it. A superb effort, my friend - one I hope you will keep up.