mean she is older then u(female). so u ask her to use 반말(/ban mal/ : intimate casual informal speech). as u know 언니(/eon ni/) is older female for female. and 말을 놓다 means "use 반말" they use 반말 to someone who is younger than u or same age as u or someone with whom u agree to use 반말 or lower social status person in korea.