Probably afraid of being called on the carpet for filing a frivolous lawsuit.
Who holds the mortgage? The "bishop".
Has it been paid? No.
Who formally, legally, holds title? The "bishop".
Is it an eviction to assert your own title? No.
Back when the Russian Orthodox Church was litigating who controlled Russian Orthodox properties in America: the church leadership in Soviet-controlled Moscow, or the church leadership that had constituted itself in America, the Supreme Court didn't work too hard to award ownership to the Soviet-controlled Russian Church.
They went for form, and did not move past it.
The lawyer is trying to find a legal grounds on which to move, and he's coming up empty-handed.
That the "bishop" violated the churches own internal canons, maybe, is something the courts will defer to the court to decide. They won't wade into the religious disputes. They'll look at who has title, formally, and who has authority, formally, and rule that way. That's the problem the lawyer has.
Now, take over the church and you've reversed the situation. You've got a bishop outside claiming possession, but a congregation inside with possession. Those in possession will only be displaced after exhaustive litigation and appeals. They will lose, eventually, but the luck may turn in the wider world and the sodomite conclave of "bishops" might have other defeats dealt unto them before the final unappealable judgment is reached.
I will be stunned if a TRO is obtained, in either direction.
Which is why the parish should take back the building.
I don't know how the "frivolity" rules in Connecticut work, but even if you hold mortgage AND the title (or a deed to secure debt), you cannot just walk in and change the locks on a tenant in possession. At a bare minimum, the bishop should have filed a dispossessory, and the parish was certainly entitled to a hearing. Contesting that is NOT frivolous by any stretch of the imagination.
In fact, I think a claim for wrongful eviction would be in order. I can't imagine that a liberal state like Connecticut doesn't have landlord-tenant laws slanted in favor of the tenant.