The strategy is to submit lots of entrants to the tournament rather than just one, then play tit for tat against all opponents except those that are in the clique. The clique players then lose on purpose to a specifically-chosen player, maximizing that players score.
If you don't want to do it this way and instead care about maximizing the total scores of the clique as a whole, you can default to every clique member always cooperating.
Even in cases where the opponent is "blind", you can use a special pattern of bets to signal that the other player is a member of the clique and then play your win-maximizing strategy once the signal is detected.
This kind of thing has real-world implications. For example: imagine a poker game with ten players, all of the same skill level and without a rake. Nine of the players can collude (say, show each other their hidden cards and make decisions based on the shared information), making it significantly less likely than a 10% chance that the targeted player will win. I suspect this is already done to an extent in extremely high-stakes games (say, $1MM+).