The letter talks about Shuly and the Marquis not having sons, and being unwilling to do so. According to some law, that's grounds for marriage annulment. However, the letter could have been fabricated or written while the Marquis wasn't in a right state of mind, as cardinal assface pointed out. By having the testimony of the uncle Count, the incluence of his mother and the letters written by Johannes is proof more than enough to prove the legitimacy of the letter.
With the marriage anulled, Jeremy becomes the head of the house and can request a duel to settle the issue. Saving his hand and honor, somewhat. The loser is Shuly, as she would be forced to abandon the Neuschwanstein house and return to her birth family, but it's a sacrifice she's willing to make.
And the church it's just butthurt that the Neuschwanstein house under Shuli is challenging them and their power.