My reasoning:
The disaster agency revealed to the press the power of the hurricane and the extent of its damage, and,with continuing rain preventing relief efforts ,it expressed fear of the welfare of the survivors.
(A) with continuing rain preventing relief efforts, it expressed fear of-meaning issue - you cannot really fear survivors' welfare ('fear of')
(B) with continuing rain preventing relief efforts, they expressed fear for they - wrong pronoun for 'agency'/ 'with' doesn't really show
...
The disaster agency revealed to the press the power of the hurricane and the extent of its damage, and,with continuing rain preventing relief efforts ,it expressed fear of the welfare of the survivors.
(A) with continuing rain preventing relief efforts, it expressed fear of-meaning issue - you cannot really fear survivors' welfare ('fear of')
(B) with continuing rain preventing relief efforts, they expressed fear for they - wrong pronoun for 'agency'/ 'with' doesn't really show
...



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