AWS API Gateway Integration Response Mapping Template using request body

I have an API Gateway resource setup with the below flow:

POST $request -> Method Request -> Integration Request -> Step Function
$response <- Method Response <- Integration Response

Currently, $response comes back as the response body from invoking the Step Function correctly. However, I want to know if there is a way I can use mapping templates to grab some values from the body of the request. For example, my request body looks something like this:

{
  "Value": {
    "Item1": "one",
    "Item2": "two"
  }
}

I would like to be able to grab the 2 properties under "Value" and return a response that looks something like this:

{
  "Item1": "one",
  "Item2": "two"
}

I have tried using the following mapping template:

{
  "Item1": $input.json('$.Value.Item1'),
  "Item2": $input.json('$.Value.Item2')
}

However, I have realised that the value of $input actually comes from the response of the Step Function (I had assumed it was the input to the entire resource).

Is there a way to access the request body in the response mapping template? The only alternative I can think of at this point is to add a Lambda Function between the API Gateway and Step Function to return the custom response after invoking the Step Function, but I would prefer to avoid this if possible.