I wish TV writers would stop with the “she’ll press charges” talk. Victims don’t press charges. Victims complain. The police decide whether to arrest. Prosecutors decide whether to bring charges. Gumb could go to the police and report that Catherine hurt her along with the B&E, but the prosecutor would decide whether to charge Catherine - which they might not, given Catherine’s past and the fact she’s already in a psych facility. As you say, pretty weak blackmail.
Also, going forward, could somebody please turn on the lights? Government offices were/are more likely to be overly bright than dim, especially back in the era of big overhead fluorescent bulbs.