Probably they said something humiliating since southern Whites like to humiliate southern blacks
We've got more enjambment here. You've got to look back to stanza 4 to understand that the "they" in line 31 refers to the people at the "big library uptown."
If we weren't totally sure from the information in stanza 4 that the people at the "big library" were white, this little stanza reassures us.
In boxing terms, this stanza is a "1-2" punch. It stands by itself to emphasize the bleakness and gut-wrenching experience of discrimination.
It also keeps this aspect of society separate from the idyllic life she lived among books and people like Mrs. Long and her own grandmother.
Notice also that this is the midpoint of the poem, so these two little lines mark a change in the tone of her narrative.
The use of enjambment between lines 31 and 32 also has an interesting effect on the visual organization of sense units. Because the adjective "southern" is left hanging at the end of line 31, line 32 stands on its own to declare simply "Whites like to humiliate southern blacks." It's as though Giovanni wants to take away the borders of discrimination to give us an accurate picture of how widespread such hatred can be.
But there's an upside to the brevity of these lines as well: they pass quickly. What brackets them is the tenacious behavior of Mrs. Long, who won't back down until she gets what she wants.