What does Mr. Pearson mean when he suggests to Squeaky it would "be a nice gesture if you were . . . to ahhh . . ."?

Previously, in the same paragraph as the given quotation, Mr. Pearson asks Squeaky if she is "going to give someone else a break this year." Squeaky wonders "if he is seriously thinking [she] should lose the race on purpose just to give someone else a break." Mr. Pearson then suggests that there are only "six girls running this year" because Squeaky doesn't give anyone else a chance to win.
In this context, when Mr. Pearson asks (or begins to ask), "Wouldn't it be a nice gesture if you were to . . . ahhh . . ." the implication is that he thinks it would be nice if she gave somebody else the chance to win the race this year. He would see such a gesture as an act of kindness. He might also be thinking of next year's race and the possibly of an even lower turnout if Squeaky wins yet again. Squeaky's reaction to this suggestion is such that Mr. Pearson doesn't even bother finishing the sentence.
Later in the story, Squeaky hears Pearson (or "old Beanstalk," as she calls him) "arguing with the man on the loudspeaker . . . about what the stopwatches say." Perhaps, in this moment, Mr. Pearson is trying to argue that someone else won the race, attempting to achieve himself what he could not persuade Squeaky to do.
Another possible reason that Mr. Pearson doesn't want Squeaky to win the race might be that he just doesn't like her. She does, after all, "call him Jack and the Beanstalk to get him mad"—or at least used to. And she does seem to talk to him in a somewhat disrespectful manner, telling him abruptly to write down her full name on his board; she gives him "such a look" of derision when he suggests that she give someone else a chance to win and storms away from him before he can finish his sentence.

Before Squeaky is about run the fifty-yard dash, Mr. Pearson approaches Squeaky to pin her number on her shirt. As Mr. Pearson checks Squeaky's name off the list and hands her the number to pin on her shirt, he casually asks Squeaky if she is going to let someone else win the race this year. Mr. Pearson proceeds to inform Squeaky that only six girls are running in the race this year and mentions that the new girl, Gretchen, should give her a run for her money. Mr. Pearson then begins to look around for Gretchen and says, "Wouldn’t it be a nice gesture if you were . . . to ahhh . . ." (Bambara, 4). Judging from Mr. Pearson's previous comment regarding the fact that Squeaky should allow someone else to win the race this year, one can infer that Mr. Pearson was going to suggest that Squeaky should allow Gretchen to win the race. Since Gretchen is the new girl and Squeaky has already won races in the past years, Mr. Pearson thinks that allowing Gretchen to win the fifty-yard dash would be a nice gesture on Squeaky's part.