I think you misunderstood the situation. In the window - list of the players to whom the invitation was sent. Now they can accept it or reject it.
The invitation could have been sent by another member of your Fellowship.
@Quercus is exactly right, those invitations sent out not invitations to join.
When they are invitations to join they have a blue arrow next to the message
When the dot is red, it means that someone in the Fellowship has sent an invitation to that player to join.
If a player applies to join the Fellowship there is a blue arrow next to the envelope