I would like to point out that Isabel's father does not explain anything to her about the "I" on her cheek.  Her father had similar scarring on his face, and its his attitude about the marks that significantly impacts Isabel.  

Isabel receives the "I" on her face when Madam Lockton decides to have Isabel branded for being disobedient.  Madam Lockton tells Isabel that the letter "I" stands for "insolence."  The mark will be a constant reminder to herself to follow orders better.  It will also be a mark that warns everybody else that Isabel is not a "good" slave.  That could't be further from the truth.  Madam Lockton is the insolent character in the book.  

Late in the book, Isabel is attempting to get the courage to engineer her own escape to freedom.  She sees herself in the mirror and looks at the brand.  It is then that she remembers that her father had large scars on his face too.  But instead of it being a negative brand, her father wore it proudly.  He said that it was a mark that made him strong.  The moment is a turning point for Isabel because she decides that she would carry her mark like her father carried his mark.  

This is my country mark.  I did not ask for it, but I would carry it as Poppa carried his. It made me his daughter.  It made me strong. 

Isabel then tells readers that the mark no longer stands for "insolence."  It stands for "Isabel."  From that moment forward, Isabel grabs hold of her destiny and engineers her own escape while freeing Curzon as well.