When Esther Greenwood goes to obtain a contraceptive device (what is described in the text as 'a fitting'), it is likely that she is being supplied with a diaphragm, a barrier method of contraception.
In 1873, the Comstock Law had made contraception illegal at a federal level in the U.S.A. However Margaret Sanger, the birth-control activist, decided to challenge this law and introduced the diaphragm to America in 1916.
Legislation regarding contraception varied from state to state, with Connecticut and Massachusetts having some of the severest restrictions. In fact, it was not until 1972 that a Massachusetts law prohibiting the provision of contraceptives to unmarried men and women was overturned.