Assuming the customer is an entity, you need a resolution from the entity to add or remove signatories. A letter from [insert any individual] does not provide you with adequate evidence of authority.
A signature card is a dated contract; it is not a fluid document which should be edited as signatories are added and removed. If your bank uses signature cards and would like to successfully offer them as evidence in the event of a legal dispute, it will require a new card be executed by all signatories whenever a signatory is added or removed.
There are no universal statutes or regulations to cite in support of the above, only the observation that the failure to do either assumes an amount of risk that a knowledgeable bank would not take.
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