How can I clean this cooking pan?
Don't clean it. 

You have the same issue as in How to remove film from stainless steel pan. This is polymerised oil, the same stuff which is intentionally built on cast iron pans. The cleaning methods listed in the linked question will also work in your case. 

But the catch is that they will also strip the teflon from your pan. So, unless you are completely sure that you can somehow clean the steel part only, without getting drops of abrasives and strong chemicals on the teflon, don't bother. It doesn't harm anything, and it surely isn't contaminating your food with anything. And if you do try something caustic on the strip, don't use it on the rim, because the strip is probably SS, but the pan's bowl is likely to be aluminium and will be corroded by many aggressive cleaning products.