In InvokeSalesforceRestApiFunction Lambda, updateRecord method can be used to update records in Salesforce.

If you haven’t setup the Connected App and Amazon Variables, please check this

https://www.infallibletechie.com/2022/11/how-to-test-salesforce-soql-from-aws-invokesalesforcerestapifunction-lambda-function-in-the-aws-console.html

Sample Payload to update Case record:

{
  "Details": {
    "Parameters": {
      "methodName": "updateRecord",
      "recordId": "5004W00002AlRM5QAN",
      "objectApiName": "Case",
      "Subject": "Testing Update from Lambda Function",
      "Description": "Sample Update Lambda REST API Testing",
      "Status": "New",
      "Priority": "Low"
    }
  }
}

Test it from AWS Console.

Output: