I have a Krampouz crepe machine made of cast iron. Someone rested what looks like a hot mug of tea on top of it, and now it has a dark brown burn patch. Does this mean it will no longer work, or is there a way I can remove this?
This is not a burnt patch, cast iron doesn't burn. It is almost certainly a rust patch.
Since the surface comes into direct contact with food, you cannot use the rust removers sold in home improvement stores. You need to remove it with lye - you can try a mechanical stripping too, but that is unlikely to get all tiny specks of rust, unless you get serious about it and use a dremel attachment until you bite into the blank metal. See also my answer here about removing rust from cast iron.
Once you have stripped that part (or all of the seasoning, if you use lye) you will need to reseason. Since this is a crepe maker, you don't have to do much with multiple layers etc., just enough to seal the surface against rust until the next batch of crepes you make. Making more batches will give you an even better surface.
Above, I said "almost sure" that this is rust. Since this is only a photo, there is a tiny possibility that this is stuck-on dirt which looks like rust. If you think that this might be the case, you could try removing it with an abrasive cleaner, or with a metal sponge. But since this will be a lot of work and the chance is small that this is not rust, you can just treat it like rust from the beginning.
1LONG before I would try lye, I would try salt. NOTE: Salt is only a chemical reactive risk to iron if left on (or soaked) in it. Dampen a paper towel, load it up with the salt dry, and try to use it to abrade it away. Salt in crystal form has a Moes hardness of 2 to 2.5, while Iron is up at 4. So the salt will (mostly) leave the iron alone, but do a good job of banging against whatever residue is there, even if it's one of the flaking iron oxides. Keep the salt as dry as you can----the damp is just to have it "hold" to the towel. When you're done, rinse obsessively while rubbing. Jul 7, 2020 at 18:22
You might also try Coca Cola (or citric acid) for rust removal. Jul 7, 2020 at 20:53
@MattKrause acid on a cast iron pan increases rust, doesn't remove it.– rumtscho ♦Jul 8, 2020 at 7:31
@tgm1024--Monicawasmistreated there are better abrasives than salt, including ones that are softer than the pan. But in fact, you want to have something harder than the pan, so you can really sand the upper layer away, if you don't want to remove the rust with lye. It's tons of hard work though.– rumtscho ♦Jul 8, 2020 at 7:39
1@rumtscho, are you sure about that? It's a pretty common method for removing rust from tools (etc): chemistry.stackexchange.com/questions/4732/… It will attack the seasoning (and, eventually, the metal too), but the rust should come off first. Jul 8, 2020 at 14:05