#O, 8 bytes

{_.@_-=}

An anonymous function that takes a character and a string.

Try it online.

##Explanation

{_.@_-=}

{      }
 _        Lowercase string
  .       Duplicate
   @      Rotate stack
    _     Lowercase character
     -    Remove all instances of the character
      =   Compare to original

O, 8 bytes

{_.@_-=}

An anonymous function that takes a character and a string.

Try it online.

Explanation

{_.@_-=}

{      }
 _        Lowercase string
  .       Duplicate
   @      Rotate stack
    _     Lowercase character
     -    Remove all instances of the character
      =   Compare to original