If Orthodox is the true Church, why do Catholics have (apparently) genuine relics?

Roman Catholics claim to have any number of *relics* which are significant to the Christian faith, of which the [Shroud of Turin](https://en.wikipedia.org/wiki/Shroud_of_Turin) is probably the best known. There also seem to be some strong arguments for the authenticity of the same. If, as they claim, the Orthodox church is the "true" church, why would God allow these (apparently genuine) relics to fall into the hands of those who have fallen away, rather than preserving them for the True Church? (I am looking primarily for Orthodox responses, though one might ask Protestants a similar question, as both believe the RCC to be in error. Also, whether the Shroud specifically is a genuine relic isn't the point as such, although "they aren't genuine relics" may be a possible *answer*.)