The purpose of Monitor bot is to monitor your bot. So in case you are a bot developer and want to keep track of your bot then you can use monitor bot to track your bot when he goes offline and come online.
To make this bot functional bot stores data which are the mentor user id, target user id and the target's last presence change time. And the last presence time gets updated whenever the target changes his presence from online to offline and vice-versa. And thats all. No more data is stored.
If you want to delete data you have stored then you can just remove the monitor or kick the bot from your server and all your data will be deleted. Also you can contact support in the official servers.