The re-rolls do not conflict, because there is no situation where the same result causes a re-roll from both effects. The Other Trickster's Shard only triggers on a successful ward save. Third Eye of Tzeentch only triggers on a ward save roll of 1. Now that the Pendant of Khaeleth is gone, there is never a circumstance where a ward save is successful on a roll of 1.
Neither of these effects "turns off" the other. They're just both subject to the general rule that no dice may be re-rolled more than once. Your opponent can argue that the rules cancel each other out all they like, but this interpretation is incorrect.