Mr. Gilmer focuses a lot on the “thirty days once for disorderly conduct” Robinson earned for getting in a fight with another black man. One argument you could make is that Robinson did not start the fight.
"What'd the nigger look like when you got through with him?"
"He beat me, Mr. Gilmer." (ch 19)
Robinson points out that he was the one who was attacked, and not the attacker. Atticus also adds that it is a misdemeanor, which is a less serious crime.
Glimer is trying to make the point that “anyone who was convicted of disorderly conduct could easily have had it in his heart to take advantage of Mayella Ewell” (ch 19). You could make the argument that the fight and the supposed attack of Mayella have nothing in common. They are in fact not related crimes.
Mr. Glimer also makes other arguments, such as about Robinson’s strength. How would you contradict those?