You don't necessarily have to go to the airport to reconfirm your airplane reservation.

Literal

Airplane [possessive-の] reservation [object-を] re-confirm [in order to-ために] necessarily airport [to-へ] go-not-even-if is-fine.

必ずしも~なくてもよい means 'not necessarily have to.' 必ずしも softens the negation from absolute to partial. ~なくてもよい is a permission pattern ('it's fine even if you don't'). ~ために expresses purpose. A useful sentence combining purpose, permission, and nuanced negation.