Try this:

import "./styles.css";
import React, { useState } from "react";

export default function App() {
// Changes made here
  const [item, setItem] = useState({});
  const [counter, setCounter] = useState(0);

  console.log("item 1:", item[0], "item 2:", item[1],item);

  const handleCounter = () => {
    setCounter(counter + 1);
  };
  const addItem = (newItem) => setItem((ing) => [...ing, newItem]);

  return (
    <>
      {Array.from(Array(counter)).map((c, index) => (
        <input
          type="text"
          key={index}
//Changes made here
          value={item[index]}
          label="Item"
// Changes made here
          onChange={(event) => setItem({...item, [index]:event.target.value })}
        />
      ))}

      <button onClick={handleCounter}>Add one more item</button>
    </>
  );
}

Instead of using an array to store the input values I recommend using an object as it's more straight-forward.

If you wanted to use an array you can replace the onChange event with the following:

onChange={(event) => {
            const clonedArray = item.slice()
            clonedArray[index] = event.target.value
            setItem(clonedArray)
          }}

It's slightly more convoluted and probably slightly less optimal, hence why I recommend using an object.

If you want to loop through the object later you can just use Object.entries() like so:

[...Object.entries(item)].map(([key, value]) => {console.log(key, value)})

Here's the documentation for Object.entries().

1. Firstly, you are using two-way data binding with your TextField component, so you also need to pass a value prop.
2. Secondly, to get the current value of TextField, we don't use this.value. Rather, the callback to onChange takes an argument of type Event and you can access the current value as follows

<TextField
...
onChange={(e) => {
    const value = e.target.value;
    // Do something with value
}}
/>

3. You cannot return multiple children from a component without wrapping them by single component. You are simply returning multiple TextField components at the same level, which is also causing an error. Try wrapping them in React.Fragment as follows

...
return (
   <React.Fragment>
   {/* Here you can return multiple sibling components*/}
   </React.Fragment>
);

4. You are mapping the TextField components using counter which is equal to the length of item array. In handleCounter, we'll add a placeholder string to accomodate the new TextField value.

...
const handleCounter = () => {
    setCounter(prev => prev+1); // Increment the counter
    setItem(prev => [...prev, ""]); // Add a new value placeholder for the newly added TextField
}
return (
   <React.Fragment>
     { /* Render only when the value of counter and length of item array are the same  */
     counter === item.length && (Array.from(Array(counter).keys()).map((idx) => (
         <TextField
          key={idx}
          value={item[idx]}
          label="Item"
          onChange={(e) => {
              const val = e.target.value;
              setItem(prev => {
                  const nprev = [...prev]
                  nprev[idx] = val;
                  return nprev;
              })
          }}
         />
     )))}
     <br />
     <Button onClick={handleCounter}>Add one more item</Button>
   </React.Fragment>
);

5. Here is the sandbox link

codeSolution: https://codesandbox.io/s/snowy-cache-dlnku?file=/src/App.js

import "./styles.css";
import React, { useState } from "react";

export default function App() {
  const [item, setItem] = useState(["a", "b"]);

  const handleCounter = () => {
    console.log(item, "item");
    setItem([...item, ""]);
  };

  const setInput = (index) => (evt) => {
    item.splice(index, 1, evt.target.value);
    setItem([...item]);
  };

  return (
    <>
      {item.map((c, index) => {
        return (
          <input
            type="text"
            key={index}
            label="Item"
            value={c}
            onChange={setInput(index)}
          />
        );
      })}

      <button onClick={handleCounter}>Add one more item</button>
    </>
  );
}

I have solved for you . check if this works for you , if any issues tell me