The Rabbit Hole

Synopsis
Back in Gotham, battling Alice and the Wonderland gang from the shadows, Kate Kane continues to be haunted by the events surrounding her sister’s death 15 years earlier. While the city holds on to hope that Batman has returned, Jacob Kane and the Crows up the stakes trying to take down the villainous crew. Kate continues to look to Bruce Wayne’s legacy for guidance as Luke Fox inadvertently gets pulled into Batwoman’s vigilante heroics. Sophie and Kate are forced to team up, while Mary finds herself in Alice’s crosshairs.

Trivia

 * This episode confirms the existence of both Wonder Woman and Robin.
 * Kate pretty casually confirms Wonder Woman exists in the Arrowverse, after many hints in the other shows. When and where she operates/operated is unclear. Themyscira Wonder Woman's birth place was confirmed to have existed in Legends Of Tomorrow episode.
 * When Vesper Fairchild talks about the incident on the bridge and questioned exactly where Batman was during the incident, and if he was at "Robin's high-school graduation". While it was probably safe to assume that Earth-1's Batman had had a Robin at some point before his absence, this line is the first time that he's actually been referenced within the Arrowverse. This name-drop comes at an interesting moment for the Arrowverse as a whole, particularly in relation to the upcoming "Crisis on Infinite Earths" crossover. Burt Ward, who portrayed Robin the 1960s Batman TV series, is going to be in the Crisis on Infinite Earths crossover event.
 * The note Beth leaves Kate "You have our father's eyes" is the line she used to reveal her true identity to Kate who was acting as Batwoman in the comics.