Logic of Wald and Zoupas' expression 33 for conserved quantities

[qinglong.1397]

Wald and Zoupas discussed the general definition of ``conserved quantities" in a diffeomorphism invariant theory in this work. In Section IV, they gave one expression (33) in the linked article. I cannot really understand the logic of this expression. Would you please help me with this?

 

[PeterDonis]

I cannot really understand the logic of this expression

You're going to have to be more specific. What about the expression don't you understand?