Ling Qingge indicated in her narration that the Duchess toured the province's cities every so often. Every decade or two, I can't remember. Point is, the visit wasn't anything special at the time that it happened, according to anything we know, and there's no reason to think that the city or the Liu who administer it are noteworthy.
Cai Renxiang submitted a formal request to have Qingge's debts re-examined as a legal matter, and someone comically high up on the food chain of the Ministry of Justice responded to it, probably after getting passed up the chain by panicking subordinates. It's possible that Shenhua interfered at this stage, but it would be highly unusual because the ministry going to her to rubber stamp a request made by her heir would be a slight against her judgement in having recognized Renxiang as heir in the first place. Heirs are pretty big deals usually, and it's unusual to have an heir that isn't a fully fledged cultivator capable of taking the reigns of the clan at a moment's notice, but considering the Cai's rank, it wouldn't do to afford Renxiang any less deference than if she were an heir in fact instead of merely title.
As for whether there's any Shenhua response to the matter, I see two main problems with the idea. The first is that I would be incredibly surprised if Shenhua wasn't already aware of the general custodianship of the Liu over their holdings. That's the kind of thing a capable Duchess should more or less be aware of. The second is that there's reasonable odds the regional minister of justice went to the Liu first and worked out a satisfactory arrangement for the affiliation of the petty thugs being whitewashed in the official report. The whole point of petty thugs is being able to throw them under the bus when convenient, and the system is nothing if not convenient for those in power.
That said, yes the Liu should be aware of the issue. Cai Renxiang only has 2 vassals, and she was able to discover significant portions of Ling Qi's background via her contacts. The Sect knew both Qingge and Biyu's identities. Amusingly they all knew all this while Ling Qi didn't have a clue. The point is, the Liu have definitely looked into who, why, and how Ling Qi is and probably feel a measure of apprehension over their shared history. Since the minor insult they suffered was already resolved, it's unlikely that they'd pursue the matter further, especially due to Renxiang's influence. It would be best for the Liu that they did not get embroiled in a feud with direct vassals of the Cai heir. Direct attention of Shenhua is unlikely and unneeded for them to feel this way.
Dammit, I'm too lazy for posts this large. Fie, fie upon you all!