It’s the first time we’ve heard it on screen. From what I can tell, it’s short for Matilda and it means “mighty in war.” I really don’t know why they chose it except that there is a Tillie in the Wonderland books, in a very small side story the Doormouse tells to Alice.
The dormouse connection seems to have been implied towards the end of the episode by Rogers, who described Tilly (after she calmed down due to her meds) that she was now “quiet as a dormouse”.
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