This is an increasingly common approach in the UK, particularly favoured by the large retailers and their copackers, but also on the increase elsewhere too.
There will almost certainly be a clause in their Ts&Cs and/or contract that defines that this will happen, and as with all such things, the Ts&Cs will also say something to the effect that you have implicitly agreed to supply according to their terms, and that they prevail to the exclusion of all others.
It's also quite possible that your own Ts&Cs may prevail to the exclusion of all others, as it's a common approach in the UK. It then potentially becomes a question of who informed who of which Ts&Cs most recently (there will probably be a statement on purchase orders, invoices etc that says "all business according to our Ts&Cs"), and whether the clause itself is reasonable, but actually resolving this becomes a daft process in which the only winners are the lawyers.
I'd check exactly which Ts&Cs have been agreed by formally signing/countersigning, if any, and see what these say on the matter.
I'd also check any specifications that you may have completed for the customer, as these seem to have an increasing number of variously ridiculous/pushy terms like this in. Don't be shy about challenging these - I now send back many specs with 50-75% of these crossed through and replaced with a statement that we don't agree to them.
Finally, and most importantly, assuming that you're in QA/technical, you should pass this to the salesperson/account manager who is responsible for the customer, as it is really a commercial rather than technical issue, and is effectively taking money out of their profit margin. This therefore gives them a good incentive to either resolve it, or to ensure that whatever prices they agree in future will include an extra bit to cover such eventualities.