If she's not trying to pawn off a fake to ingratiate herself, maybe Medusa wants BREW to be in Shibusen, right next to all of the other Eibon Tools. If it is more convenient for them all to be in one place, perhaps she believes she will have greater access to it once she is already inside the walls of the building. She may have even laid a trap on it or around it so that if it gets near something, some contingency she set activates.

By the way, is she still possessing that little girl's body, or is this her own re-formed one?