A person who pulls himself up from a low environment via the boot-strap route has two choices. Having risen above his environment, he can forget it; or, he can rise above it and never forget it and keep compassion in his heart for those has left behind him in the cruel up climb. The nurse had chosen the forgetting way.
These lines he come right after the doctor administering Francie's vaccination makes his cruel comments about the filth of poor people. Francie sees the nurse as a mother-figure, and keeps thinking she will defend her. A classic fall from innocence scene, the vaccination chapter foreshadows who Francie will become. Francie will choose the second option—to keep compassion in her heart. Like the nurse, Francie will not live in the slums her whole life, but when she leaves Brooklyn at the end of the book, she refuses to forget her childhood, and her home. "Forgetting" comes up another time in the book as well, when Francie loses Lee to his fiancée. Katie tells Francie she will be happy, but will never "forget."