I can't talk for the mobile apps, but in the Flash PC version, the owner gets an indication of the new applicant in the left column - where also friend requests are. There, you may accept this application.
"Pending" players at the bottom of the members list don't mean anything AFAIK. IMHO, these are "leftovers" from unsuccessful member applications and invitations (when the owner invites the player but he refuses). I have even seen player's names both as proper members and as pending at the same CC.
I've always deleted them.