I hadn’t really thought about it, but I would guess it became a matter of pride, both professional and personal. Professional in that he was hired to do something and failed, so he feels like he needs remediate his professional reputation. Personal in that Makoto broke his prized knife, so he went out and got it repaired or another one to use as the weapon of choice to go after Makoto again.

Tbh, I think the more important plot point from this encounter is how unfazed Makoto is by killing and disposing of the assassin bodies. It was a big moment in season 1 when he killed his first hyuman, but I think this is supposed to help us to recognize a way in which Makoto has changed since then.