you have to have fat on the diet otherwise alli doesn't do anything since it doesn't work on carbohydrates or protein.
So olive oil is one of the best. it's a perfect monounsaturated fat - as you said "drizzle" which is perfect since oils inherently are entirely fat so you can't go crazy. Even though it's a healthy fat, it doesn't fall into another category. So, some of the oil will stay in the pan, etc.., but some will be absorbed by the food and you will need to guestimate, primarily to avoid treatment effects and consuming hidden calories that slow your weight loss. Don't need to be fat phobic since you need to eat fat to lose fat. Be aware that whatever your protein you might be having at that meal may also contain fat. While it should be lean, it still has some fat that should be accounted for.
skinless chicken *** might not have as much fat as wild salmon does, but on the other hand, the salmon has heart healthy omega 3 fats while the chicken doesn't. So the fat is critical for health reasons and for the feeling of fullness and satiety they bring. Just keep in mind, it's present in a lot of animal protein type foods too.
But, if you are cooking in oil, that counts too, so i try to minimize that and use it on a salad or other veggies.
Depending on your total calories, the fat should be 30% of your daily caloric intake and the oil as well as any other fat you consume is part of that total.