The basket occasionally went in the dishwasher which cleaned the surface, but the well gunked grease has been building up.
Tried soaking the basket in soap and hot water. Scrubbing with a soft sponge. And then running the dishwasher multiple times but it only got a small part of the grease out.
Is it teflon coated? If so you should be careful. Many of the suggestions here are for increasingly abrasive options which will scratch that coating and cause it to eventually flake off, which means it will get into your food, which definitely not something you want to eat
On one hand the grease itself is probably not a food safety issue anymore. Similar to a cast iron pan once oil/grease heats enough on a surface it polymerizes and essentially bonds to the surface. This is generally safe unless the oil is exposed to very high temps (beyond what is typically used for cooking) but it looks bad on stuff like sheet pans
However you do want to be a bit more diligent cleaning as a result. Unlike a cast iron pan where the polymerization layer (seasoning) is generally very smooth this is generally not; it is bumpy and has more nooks and crannies. This means there are more areas where filth and bacteria can be harbored. Not a huge issue, just make sure you clean well.