Fly in the Omelette

I fried an omelette and saw that there was a fly in it. What is the status of the pan?

The omelette is permissible to eat after removing the fly (and there is no concern that the fly laid eggs in the omelette as that is not its nature), and the pan does not require koshering since the fly imparts a detrimental taste.

The Shulchan Aruch, Yoreh De'ah, Siman 104, Paragraph 3 states: "Repulsive items, which a person's soul detests, such as ants, flies, and mosquitoes, from which everyone refrains due to their repulsiveness, even if they are mixed into a dish and their bodies are dissolved into it, if the permissible part is greater, they are allowed. Nevertheless, whenever possible to check and remove with a sieve, one should check and sieve." This means they do not prohibit the dish by taste, only by majority, as it is a detrimental taste, similar to the mouse mentioned in Avodah Zarah 68, when a mouse falls into beer or vinegar, there is concern it imparts a pleasant taste, but in other liquids, Rambam and others write it imparts a detrimental taste. And so too with a fly in other liquids. See Taz there, s.k. 6, who writes in the name of Bach and Maharshal to be stringent, as they are concerned it imparts a pleasant taste. And Rema has already written in Siman 107, s.k. 2, that the custom is to be lenient in this.