USCIS agent called me back and said the holdup with CBP is likely because this beneficiary previously broke parole.
My beneficiary was previously paroled into the United States through U4U but had to leave after 3 months to attend to her dying mother. We applied for travel authorization (advanced parole) but it wasn't processed in time, denial came 1.5 years later. We didn't know about the opportunity to apply for emergency advanced parole which has a much quicker response time.
USCIS agent said that the good thing is that she didn't receive a denial from CBP yet. But gave no timetable on when we can expect an answer to be given.