Here is how this can be done, note that we have to use onkeydown which fires when a key is being pressed, but not before it is being released (this way we can intercept and prevent the key stroke from being taken into account):

function MyInput() {

  const containedChange = (event) => {
    if (event.key.length === 1 && event.code.startsWith('Key') && event.code.length === 4 && event.target.value.indexOf(event.key) !== -1) {
      event.preventDefault()
      return false;
    }
    
    return true
  }
          
          
  return (
    <input
      id="input"
      className="App-Contain-Input"
      name="containedLetter"
      type="text"
      onkeydown={containedChange}
    />
}

A way to do it with a cheeky two-liner is to get rid of any non-letters with regex, then let Set do the de-duping by converting to Array => Set => Array => String:

As a side note, many of the other solutions posted here make one or both of two assumptions:

1. The user is only ever going to edit the last character... but what if they edit from the beginning or middle? Any last character solution will then fail.
2. The user will never copy/paste a complete value... again, if they do, most of these solutions will fail.

In general, it's best to be completely agnostic as to how the value is going to arrive to the input, and simply deal with the value after it has arrived.

import { useState } from 'react';

export default function Home() {
    const [value, setValue] = useState('');

    return (
        <div>
            <input
                type='text'
                value={value}
                onChange={(e) => {
                    const onlyLetters = e.target.value.replace(/[^a-zA-Z]/g, '');
                    setValue(Array.from(new Set(onlyLetters.split(''))).join(''));
                }}
            />
        </div>
    );
}

One pure js solution would be to handle the input value in onkeyup event where we have access to the latest key as well as updated input target value.

If the latest key pressed is duplicate then we will found it on 2 location in the target value, first on some where middle of the target value and second at the end of the target value. So we can remove the value at the end (which is the duplicate one).

The below code snippet shows the implementation of above in React

const Input = () => {
  const handleKeyUp = (e) => {
    const { key, target: { value }} = e;
    const len = value.length;

    if (value.indexOf(key) < len - 2) {
        e.target.value = value.slice(0, len - 1);
    }
  }

  return (
    <div>
      <label>Unique Keywords</label>
      <input type="text" placeholder="my-input" onKeyUp={handleKeyUp} />
    </div>
  );
}