The issue is the quote is being sent in the HTTP request inside the JSON object.
I fixed the script in your bot Chatter to add,
input.toString().replace('"', '\"')
>>
json.messages.add({"role":"user", "content":(conversation.getLast(#input, 1)).input.toString().replace('"', '\"')});
This will fix it for now. We will also update our HTTP code to automatically escape quotes for all JSON objects.