As Bishop of Troyes, Pierre d’Arcis held the highest ecclesiastic position in the city and the surrounding area, which would’ve also including Lirey.
In the Catholic Church, a bishop is an ordained minister who holds the fullness of the sacrament of holy orders and is responsible for teaching doctrine,[1] governing Catholics in his jurisdiction,[2] sanctifying the world[3] and representing the Church.
https://en.wikipedia.org/wiki/Bishops_i … lic_Church
Bishop, in some Christian churches, the chief pastor and overseer of a diocese, an area containing several congregations.
https://www.britannica.com/topic/bishop-Christianity
All Christian laypeople under the jurisdiction of the local bishop should submit to the spiritual authority of the bishop.
bishop. The highest order of ordained ministry in Catholic teaching. Most bishops are diocesan bishops, the chief priests in their respective dioceses. But some (auxiliary bishops) are the top assistants to their diocesan bishops, and some priests are made bishops because of special posts they hold in the church, such as certain Vatican jobs. Diocesan bishops and their auxiliaries are responsible for the pastoral care of their dioceses. In some cases diocesan bishops are assigned a coadjutor bishop, who is like an auxiliary except that he automatically becomes the diocesan bishop when his predecessor resigns or dies. See auxiliary bishop and coadjutor. In addition to their diocesan responsibilities, all bishops have a responsibility to act in council with other bishops to guide the church.
https://www.usccb.org/offices/public-af … olic-terms
One would expect d’Arcis to have the authority to tell people what to do in church in his diocese. Since Lirey was part of it, if the bishop in Troyes commanded for the Lirey church to not display a relic, it was under their obligation to obey. And if a person continues to sin, the local bishop had the power to excommunicate anyone in his see.
“The authority of a bishop to excommunicate someone was restricted to those persons who resided in his see.”
https://en.wikipedia.org/wiki/Excommuni … lic_Church
During the Middle Ages, excommunication was analogous to the secular imperial ban or “outlawry” under common law. The individual was separated to some degree from the communion of the faithful.[14] Formal acts of public excommunication were sometimes accompanied by a ceremony wherein a bell was tolled (as for the dead), the Book of the Gospels was closed, and a candle snuffed out — hence the idiom “to condemn with bell, book, and candle.”
https://en.wikipedia.org/wiki/Excommuni … lic_Church
So, what is strange is why would there be a need for a bishop to appeal to the Pope that someone is not doing something correctly in church? If someone was sinning, then the bishop had the power to excommunicate. If anything, what we should see is a memo from Charny to the Pope for an appeal, not from bishop d’Arcis to the Pope asking for assistance.
https://debatingchristianity.com/forum/viewtopic.php?p=1109439#p1109439