If your status is red , you are unable to receive game invites anyway. Only when it is Green or Blue.
Once you receive an invite to a game, you click on it and there are 2 options to decline.
1 - already in a game - doesnt allow for a further message
2. No Thanks, once this is selected, you can type in a short response.
If you are in fact already playing in a game, your should switch your status to RED.
Check that it is Green again, once the game is over.