This looks like an enquiry at cross purposes. I am also very suspicious about the original message.
You don't say if the notice was by letter or electronically - if the latter I'd be even more suspicious.
I've had many communications from the bank that look very convincing at first sight... though the dead giveaway for most is that the bank is not mine!
Why would you expect house insurance to cover guarantees? You tell us the letter cites warranties on domestic appliances, not property including those appliances.
Warranties cover the equipment failing through no fault of the owner, and are met by the manufacturer, via the retailer; not the home insurer. An extended warranty or a "service agreement" is a specific insurance policy with the manufacturer, not your house insurer.
However, the Home & Contents policy might cover consequential damage, warranty or not.
Your policy document should explain it. Assume anything not mentioned specifically, or implicitly by category, as not covered. Warranty repair might even be listed as excluded, to avoid duplication. It is limited to repairing or replacing the appliance only, and at the manufacturer's risk. Warranties exclude breakdown by misuse, abuse or modification; and the home-insurance would exclude both the appliance and consequential damage.
Repairs or replacements during the guarantee period but due to external accidents such as flood or fire might be covered. Those are not warranty claims.
Poor Becky probably thought you were asking about property insurance until you demanded to know if it covers the guarantee. I think you were wrong to have been so abrupt.
If I am right, you had only to have examined your policy document, then telephoned your bank if you were still not sure; but importantly also to explain why you are asking.
Becky told you warranty claims are not covered - as I would expect - so why would the bank have sent you that letter? You must report it!
In any case, there was no need to have been rude to a staff member who was trying to help you.
I am sure it looked very convincing, but had you actually considered if that original communication really was from the bank....?
