I have a grill pan with some cooking residue on it. I'm not exactly sure which food caused it (usually oven cook chips, pizza or grill sausages, burgers, sometimes mackerel) but something left this and I'm struggling to clean it. It's very black, and also very smooth. It's been in the dishwasher, soaked in washing up liquid and also tried sodium percarbonate on it. I've tried scrubbing with both a sponge (rough green side) and some natural scrubbing thing we have. Nothing has touched the perfectly smooth finish and removed any of it. The only way I've found is to scrape it off with a metal utensil. I successfully removed quite a lot (just the right amount of pressure makes it lift ok) with a wide palette knife. But this method is high risk when it comes to scratching the non stick coating off, so I'm looking for a safer alternative if anyone can help?  
This is polymerized oil - the same stuff that people build up on iron pans as seasoning. There is no good way to remove it from a coated surface. It is quite resistant to both chemical and physical methods, as you discovered. Most mechanical methods will scratch your existing coating, and as for chemical methods, the only reliable one is lye. If the existing "nonstick coating" is enamel or teflon, it shouldn't be damaged by the lye, but we cannot tell for sure from a picture. You can also leave the spot there. The problem is purely cosmetic, it is perfectly well suited as coating for a pan (as said above, it is created on purpose on reactive surfaces). 