Think of the MOTD window as a simple web browser. If you want to send a particular player's information to a website that is being shown, you'd need to encode that information into the URL.
For example, if you want to send a player's SteamID, you'd send them to a url like this:
But you would dynamically format the URL string to include the player's actual SteamID. Also, if you are going to be sending generic text (text which you are not 100% all of the characters it might contain) then you need to first URL encode the text before putting it in the URL.
If you don't do this then there won't be any game-specific information sent. However, as with all websites, the website can still get your IP address and anything therefore derived.