It is their job to collect the fee from your credit card. You've done your moral duty by notifying them.
Just a word of warning though, this happened to me once and the company eventually got around to charging me about 20 months later. So a huge credit card bill arrived at a time that was unexpected and difficult for me to pay off by the end of the billing cycle.
I normally pay the balance off every month in order to avoid debt and interest, but the unplanned nature and sheer size of the delayed charge meant that I could not do so that month. So their screwed up billing practice actually cost me more money than had they just billed normally.
Since this sounds like a large purchase (appliances), I would reserve the money to pay for the appliances for quite some time. I think in financial terms this means you cannot treat the money as an asset because you have a pending liability against it. (Of course if you are well off and the amount is trivial to you, then this doesn't matter.)