Mr. Gilmer begins by commenting on Tom Robinson receiving a misdemeanor for disorderly conduct and incorrectly assumes that Tom won the fight. Mr. Gilmer then shifts the topic to Tom's strength and elaborates on his ability to easily destroy a chiffarobe with his one hand. He then asks Tom if he is strong enough to choke the breath out of a woman. Mr. Gilmer then questions Tom Robinson on his motives for helping Mayella and suggests that Tom had his eye on Mayella for a long time. When Tom Robinson truthfully admits that he helped Mayella out of the kindness of his heart because he felt sorry for her, Mr. Gilmer realizes that he has the upper hand. Mr. Gilmer then proceeds to manipulate the jury's racial prejudice by attempting to make Tom admit that Mayella is lying. Mr. Gilmer realizes that it is taboo and unacceptable for a black man to accuse a white woman of lying and encourages Tom to admit that Mayella is fabricating her story. Mr. Gilmer then proceeds to ask Tom why he ran if he did not commit a crime and begins to refer to him as "boy."

One could argue that Tom's single misdemeanor does not make him a violent criminal, capable of assaulting and raping a defenseless woman. Another argument to refute Mr. Gilmer's claims is that Tom's strength and ability to bust up furniture does not make him capable of inflicting the specific injuries to Mayella's face, head, and neck. Even if Tom was strong enough to throw Mayella on the ground, one could not explain the handprints encircling her neck given that Tom only has one functioning arm and hand. One could also argue that given Tom's clean background and positive reputation, his offers to help Mayella were genuine. Another argument to refute Mr. Gilmer's claims is that he is simply manipulating the jury's racial prejudice in the hope of winning the case.

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?