Honestly, who knows why the last babysitter quit, but that gave the new opportunity to find another.

Damian, with his 6 year old daughter ritza, Had maybe driven the babysitter to quit unintentionally, But he needs someone to look after her when he's out as Batman.

“I need you to look after her while I'm gone. Your name?” The statement itself was brief and short, everything already discussed over the phone. not like he's gonna tell them he's batman.