Wouldn't that be the inner labia, or am I mistaken?
It's the clitoral hood.
Female circumcision, commonly known as
female genital mutilation (fgm), is the removal of this, as well as much more of the exterior genitals.
It's illegal in a lot of countries, but is popular among people of North African or Middle Eastern descent, as well as several other countries.
It's considered a Human Rights Violation by the UN.