Establish what kind of extractor you have first, because Gaggenau sells downdraft and island units alongside canopies and their filters are in different places. Nothing abrasive touches any external surface, and stainless is worked along the grain.
Gaggenau extraction is frequently not a canopy hanging over the hob, which is why these get neglected more than any other appliance in an expensive kitchen.
Downdraft and island units hide their filters
A downdraft module rises out of the benchtop beside the cooking surfaces, or sits flush in it, pulling vapour sideways. A island unit hangs over a benchtop with no wall behind it, often as a sculptural slab rather than an obvious hood.
Both carry grease filters exactly as a canopy does, and both load exactly as fast. The difference is entirely psychological: a canopy with visible filters overhead reminds you it exists every time you cook, and a downdraft slot flush in a benchtop does not read as an appliance at all.
So the first job is establishing where the filter actually is. On a downdraft it is usually behind the rising panel or under a removable trim in the channel; on an island unit it is on the underside as normal. If yours has never been opened, that is where the smell is coming from.
Nothing abrasive, and along the grain
Gaggenau extraction is solid stainless and anodised metal, and it marks permanently. Warm soapy water and a soft cloth, worked along the brushed grain, never across it. On an island unit hanging at eye level in the middle of a room, swirl marks are visible from every angle rather than one.
The rest of the method
Filters soaked flat in hot water with a non-caustic degreaser, then the impeller housing behind them, with the power isolated first. Our rangehood cleaning guide covers it in full.
What actually goes wrong
A downdraft never opened, because it does not look like an extractor.
Swirl marks on an island unit, visible from all sides.
An abrasive used on anodised trim, which cannot be polished out.
Should you do it yourself?
Do it yourself for the filters and external wiping, along the grain.
Get someone in for the impeller housing and check they are insured, for the same reason as on the Gaggenau oven and Gaggenau cooktop.