Yes, it is probably 30 EUR or so. However I thought there might have been a simple, safe solution, like in cleaning silver with salt + aluminum, but I probably just buy a new one instead...

Yes, aluminium is more common, but since I have an induction stove, I bought the stainless steel variant. Sadly, the induction stove is very, very efficient. This never happened with my aluminium Bialetti on a gas stove.

As a comment after severalt months: The wood soap helped a bit, but in the end, we just applied some teak oil to the table. We did not plan on preparing it with any oil, but it worked out quite ok. During the winter, the wood shrunk a bit due to the dry air, so we had a carpenter fix it up again, and the table looks fine now.

The table is made from recycled Teak, and had not yet been prepared by anything. We used a mild wood soap to clean off whatever was left on the top, and now we'll see how the wood manages.