A new mortgage lender with the bank wants to send letters to former customers - are there any issues with this?

Don't know of any issues as long as he or she is not under a non-compete clause and they did not bring any customer's private information with them from previous employer. Have done these sorts of letters for a couple of different places I have worked.

Normal advertising rules would apply as these are not follow-ups to questions they have asked you. Also, look for any opt-out lists you may have for people who may have asked you not to contact them in the past.