The Scarlet Egg is one of two eggs found near the end of Silent Hill 2. James Sunderland obtains the egg after defeating the two Pyramid Heads in the first floor lobby of the Otherworld Lakeview Hotel after coming to terms with his guilt.
The connection the eggs have to Pyramid Head and James isn't specified in-game, but they are both used to unlock the doors leading to the final boss. Once both are inserted into the lobby doors, they will unlock and grant access to the final hallway.
The scarlet egg could symbolize Maria, as she could be represented as "new", "healthy", "beautiful", and "alive", while the rust-colored egg could represent Mary Shepherd-Sunderland, who is "old", "diseased", "ugly", and "dead".