Technically the oil pump suction filter, which is there to protect the oil pump, which then delivers the oil to the discharge filter, the one you change at a service, which protects the engine. At some point the oil passes through the oil cooler which is cooled by the water of the engine coolant, as opposed to an air cooled oil cooler of earlier models and manufacturers.
This allows quicker warm up of the oil.
When the blue light goes out on the dash it means the coolant is up to temperature, but not necessary the engine as a whole as the oil takes longer to reach optimum temperature. When they are both 70-80° C then the engine is up to temperature.
This also means just because the blue light is extinguished you can give it the beans, but niether does it require idling the engine to warm it up, as you are doing more harm than good. Never mind if the heater is not blowing hot, (wear suitable clothing for the weather).
Easy acceleration without overloading the engine in too higher gear and proceeding steadily until both oil and coolant are up to temperature.
Garaging the car in all weathers is beneficial to the car in several instances, particularly on cold and frosty mornings.
Start the engine, drive out of the garage, close the doors, put on the seat belt and you are ready to roll. If parked outside, clean the ice off the windows first, before starting the engine, better still cover the windscreen with an old shower curtain.
The oil not only lubricates, but cools the components it lubricates and also takes with it acids due to the combustion process, more so with these engines, with the regen cycle, hence it is important to use a C2/C3 rated oil which has a low ash content when burnt in the dpf but also a high TBN to counteract the acids and fuel blown down the bores during partial regens.
Removing the oil pump suction filter which I understand is plastic is not a simple job as a lot of other stuff needs to be removed to get access to the flange bolts, poor design, or designed like that on purpose to put off DIY enthusiasts and increase profits to the dealer network.