How is a utensil or pot, in which the meat of a dead animal was cooked, purified when the food was greasy, and what is the ruling on the grease remaining in it after it has been washed?

Purifying a vessel from impurities is done by pouring water over the impure spot and increasing the water until the traces of the impurity are removed. If any grease or fat remains, it must be washed until its trace is completely removed. And if the fat is not removed except by using soap or the like, then its use becomes obligatory to remove the impurity.