What she means:
In the opening act of Bioshock Infinite, the Lutece twins have a messenger boy give Booker a telegram telling him not to enter the raffle, because every time a Booker enters, the city sees the mark on his hand that makes him the False Shepherd. Why couldn't they have sent him a pair of gloves instead?
3. Robert and Rosalind Lutece are the same person but from different universes and while they are very similar, there are some key differences between them. Rosalind shows at various points throughout the game that she is colder than her “brother”, a bit more serious and cynical. Both characters reached the same place in their careers, but everything Robert did, Rosalind had to do as a woman in the early 1900s and the game is reflective of the fact she would have had to be a harsher person to get where he did.