JSFiddle - React, Tailwind, and code Playground

HTML

<div class="options">
    <div><input type="text" name="option[]" value="Option A"> <a href="#" class="delete_option">Delete</a></div>
    <div><input type="text" name="option[]" value="Option B"> <a href="#" class="delete_option">Delete</a></div>
    <div><input type="text" name="option[]" value="Option C"> <a href="#" class="delete_option">Delete</a></div>
</div>
<a href="#" class="new_option">Add a new option</a>

JavaScript

jQuery('a.new_option').click(function(){
    jQuery('div.options').append('<div><input type="text" name="option[]" value=""> <a href="#" class="delete_option">Delete</a></div>');
});

jQuery('document').on('click','a.delete_option',function(){
    jQuery(this).parent('div').fadeOut();
});