Customer has opened chargeback as we haven’t responded over bank holiday. Now wants the parcel. Refund or ship?

Hi all, honestly at the point where l I just assume people are out to cause problems.

A customer placed an order with us on the 29th March (we have a 2 week turnaround). On Thursday (3 business days after placing her order) at 7:02pm (after closing for the bank holiday weekend) she emailed to ask about a delivery date. She then tried calling today (from the contact page stating it’s closed on weekends & bank holidays) to which she got no response, obviously, as we are closed. She then decided to send an email threatening etc as she hadn’t heard from us (after only trying to contact us after closing for a bank holiday weekend).

I was just checking the emails & saw this pathetic string of emails so replied saying we’ll get back once we’re in as we’re of course closed for the bank holiday. Only for her to reply with she’s opened a chargeback but will put a hold on it until a delivery date is confirmed. Is it worth even entertaining it? Given she’s obviously problematic and now raised a chargeback for no response (on a bank holiday) what would you guys do? It’s a couple hundred pound.