Homura finds it after she's released from the hospital. It turns out Madoka used her wish to save it after it was hit by a car. Madoka then asks Homura to take care of it in case something happened to her (dat death flag). On Walpurgisnacht, the cat leads Homura to Madoka.
Turns out it was just an another troll device by Shaft (much like the OP), but they asked Urobuchi to include it in the Drama since it was already drawn and everything.
Then again, considering the OP lyrics make perfect sense in connection (no pun intended) with Homura's point of view post-ep 12, it's not that much of a troll really.