The ARC Raiders Items "Greasing Her Palms" quest, given to you by Celeste, is a little different to most of the other quests you'll have completed so far. This is because most quests all take place on the same map, so you can complete them in one raid, but "Greasing Her Palms" sends you all over the Rust Belt, to three different maps, which inevitably means it'll take a little longer to complete.
You must visit specific locations on Dam Battlegrounds, Spaceport, and Buried City to complete this quest, one of which requires a key… although thankfully, you are given that key upon accepting the quest. All three of these locations can have fantastic loot, so we'd recommend heading in with at least one safe pocket, especially for the first location so you don't lose the key if you die.
With three locations to visit on three different maps, all you need to do to tick off each objective is enter the designated room. If someone has beat you to it and all the loot has gone, don't worry, because you can still complete the quest. Here are the three locations you need to visit on Dam Battlegrounds, Spaceport, and Buried City.
First up is the locked room in Water Treatment Control on Dam Battlegrounds, which, despite needing a key to unlock, is probably the most straightforward of the three because it tells you exactly where you need to go. Head to the named Water Treatment Control landmark near the center of the map, then make your way to the middle floor. This building isn't particularly big, but you'll find the locked room in the eastern corner, which you can see in the image above. Unlock it with a key or just head inside if someone else has beaten you to it and the task should be completed.
For the rocket thrusters on Spaceport, you don't actually need to do cheap ARC Raiders Coins anything specific beyond go to a location. Even though the objective says you need to "scope out" the rocket thrusters, all this means is you need to hang around there for a few moments until the task is complete.