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Thank you for your question and welcome to Just Answer.
What you are observing is not pus. Most if not all of any infection present around that tooth came out of the extraction socket within minutes of the tooth being removed.
Once a tooth is extracted, the resulting hole fills with blood and clots. This blood clot is the matrix from which your body creates the new bone and gum that will fill in the space left by the extracted tooth. As this blood clot matures and becomes more fibrous, it can appear to have a white film or skin over the top of it. This appears as a white spot in the center of the healing socket. This is nothing more than new gum tissue being formed and because this layer of the clot is exposed to the saliva in your mouth, it becomes saturated with moisture, waterlogged in a way, and appears white. This is perfectly normal and will disappear as the healing progresses. Do not poke at it or disturb it at all if you can help it. Your are doing all the right things with your salt water rinses and keeping it clean. I hope this answers your question.
If you have any concerns regarding this issue that I have not addressed, please let me know and I will get back to you with more information.
George McKee DDS