However, they also did this to Protestants, after a while, and with so many French Huguenots wearing fleur de lis brands, it lost a lot of its former meaning. The English branded people with marks, in different locations, depending on what they were accused of. This punishment came into the laws in the reign of Henry VIII, and was abolished in the 18th Century, when they started getting heavily into transporting folks to the colonies. Based on my experience with burning my fingerprints off on an antique stove, and the fact that the pain lasted for weeks, you might not want to get into that. The surrounding skin, with years, will eventually fill in areas that haven't been too badly damaged.
Third degree is slightly better, due to cauterization.
Where it gets you is if the scab cracks. Brands tend to spread 2-3 times the width of the iron. The length of steel is rarely more than an inch long. BTW the most famous brands that people remember were of the forehead brands that the followers of Charles Manson wore during the Helter Skelter trials. The fleur de lis brand is a prominent part of the plot, and is shown on the character played by Rebecca DeMornay.