How to filter out what gets returned to client when invoking api gateway?

I have api gateway integration with step function. When I invoke it I get in a response more than I want to return to client. How do I filter out what gets returned to client? I only want values in "output" field. Currently, I get following

{
  "billingDetails": {
    "billedDurationInMilliseconds": 200,
    "billedMemoryUsedInMB": 64
  },
  "executionArn": "arn:aws:states:us-east-1:0935357777988:express:mystatemachine-stag:d12cb1cd-2094-4690-91f6-31af336e1d0f:42fd1794-c810-46d2-a60d-bb68ed5ad31c",
  "input": "{\"pzId\":\"01GQTJW20W5J99R0ZXD1T3W0Q6\"}",
  "inputDetails": {
    "__type": "com.amazonaws.swf.base.model#CloudWatchEventsExecutionDataDetails",
    "included": true
  },
  "name": "d12cb1cd-2094-4690-91f6-31af336e1d0f",
  "output": "{\"details\":{},
  "outputDetails": {
    "__type": "com.amazonaws.swf.base.model#CloudWatchEventsExecutionDataDetails",
    "included": true
  },
  "startDate": 1.686226844882E9,
  "stateMachineArn": "arn:aws:states:us-east-1:0935357777988:mystateMachine-stag",
  "status": "SUCCEEDED",
  "stopDate": 1.686226845062E9
}

If you are using API Gateway HTTP APIs, you cannot (to the best of my current knowledge) manipulate the response from the Step Functions API. You can with API Gateway REST APIs.

With REST APIs, you can use a Mapping Template in your response configuration to return. For example, you can use the $input.path function to provide a JSON Path expression that will grab the output key.

$input.path('$.output')

You can also check out this documentation page that describes how to use the StepFunctionsRestApi CDK construct to simplify setting this integration up.