I agree with you, I think verse I makes it rather obvious: the woman cannot pray, I imagine the "sieve of her hands" suggests she's holding her face in her hands in despair, then she raises her head at the sound of a prayer sung by a tree.
The whole poem seems to say that when people become unable to pray (I think, unable to form coherent words to express a prayer), the sounds from the world around them become prayers, perhaps more adapted to the world because they are made up of meaningless or incoherent sounds, the only way to express the prayer, in a world that has become... well, too complicated? detached from religion?
Hmm, I'm not sure that was very clear. ;)

I'm an atheist, not even baptised (and raised in a Protestant city), by the way.