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#05AB1E, 7 6 4 3 bytes

Code:

l`-

Explanation:

l     # Convert both elements to lowercase
 `    # Flatten the array
  -   # Loop over the second line of text and substract each char from the first character
        For example: "abcde""ba"- would result in "cde"

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Truthy is when the current letter is outputted. Falsy is when nothing is outputted.