Filtering user input to not contain a specific character
Your code looks correct and safe to me.  However, I would simplify it as:

public static String filterInput(String userInput) {
    return userInput.replace("\u00b6" /* Pilcrow sign */, "");
}


Two public functions seems like overkill, when all you need is a static function.  (If you intend for the filter to be configurable by overriding checkCharacter() in a subclass, then I would suggest changing to a more flexible design where the naughty characters are specified as a parameter.)