They just laugh at him, threaten him, and finally dismiss him. (Probably a good idea, considering that they almost killed each other.) The poet points out that he has lived longer than they have and might have something to teach them. He asks them to love each other as brothers and suggests that they shouldn't be alone together. The final poet we encounter shows up outside Brutus and Cassius' tent after their quarrel. Even after the mob realizes he's not that Cinna, they kill him anyway as punishment for his "bad verses." (That the mob is ignorant enough to be this blood-lusty casts some doubt on whether they're qualified to be literary critics.) Next we see Cinna the poet torn to shreds for having the wrong name.
Caught up in his affairs of state, Caesar ignores this learned man's teaching, which costs him his life. The first and only person who can explicitly warn Caesar in detail of the plot to kill him is a teacher of rhetoric, Artemidorius. Within that context, the presentation of the men of letters in Julius Caesar makes a little more sense.
The idea of writing for writing's sake wasn't popular. Livy's History of Rome, Caesar's own Gallic Wars, Tacitus' Histories, and Virgil's Aeneid had history at their core. The most important pieces of literature from that time, whether poetic or not, focus on history and tradition. While Shakespeare's work was considered important enough to get him royal patronage from King James I, poetry during Caesar's time was decidedly different. These purveyors of words aren't central to any of the play's action, but they do stand out because of how widely they're disregarded, even when they have important things to say.