We can assign the string to the variable and it treats as objects. Using objectname.keyname i.e (json.caller_id), we can get the value.
<!DOCTYPE html>
<html>
<body>
<script>
var json = {"dispnumber": "+XXXXXXXXXX", "extension": "1", "callid": "b7d14b81-68cf-4250- b5f2-fe486ef7b0b6","destination": "+911762503777", "caller_id": "+91XXXSSSSSS", "action": "phone", "event": "connected"};
alert(json.caller_id);
</script>
</body>
</html>
We can also get the value by making it string and using JSON.parse converts into object
<!DOCTYPE html>
<html>
<body>
<script>
var obj = '{"dispnumber": "+XXXXXXXXXX", "extension": "1", "callid": "b7d14b81-68cf-4250- b5f2-fe486ef7b0b6","destination": "+911762503777", "caller_id": "+91XXXSSSSSS", "action": "phone", "event": "connected"}';
var json = JSON.parse(obj);
alert(json.caller_id);
</script>
</body>
</html>