The hint said "Please change the oil of the lamps towards the back entrance. Rumi has changed the other ones already. The old oil burns brighter, get that done as soon as possible." Meaning follow the bright lamps to get to the entrance
But if Rumi has already changed the oil, and he's telling her to change the oil near the rear entrance it would mean that the rear entrance is where you want to go so you head toward the dimmer lamps.
I guess you define rear entrance as where they are coming from where I saw it as where they are trying to get to.