@Greg Lees. They're probably referring to the Due on Sale/Transfer clause that's found in most mortgages. This is a Fannie Mae/Freddie Mac requirement, not necessarily a bank requirement. However, if your lender plans on selling your note on the secondary market to Fannie Mae/Freddie Mac or to another bank that plans to do the same, this language is generally included in the mortgage paperwork. Essentially, this says that if you transfer or sell the Title to your property, the mortgagee (lender) as the right to call the entire principal balance due immediately. Just because they have the right to do this doesn't mean that they will exercise that right. In fact, I've personally never heard of a bank doing that so long as the mortgagor (the borrower) continues to pay their monthly payments. Transferring the title from your personal name back into an LLC after closing is something I'd probably not mention to the originator, as they're required to tell you that you ought not to. There's plenty on this specific topic floating around the forums.
Bottom line: If you're paying your monthly payments, banks generally don't enforce this clause. Why? because as long as you continue to make payments, they're making money, and so are the GSEs etc. They don't want to risk spending tons of money going through foreclosure on a performing note just because of a transfer/due on sale clause.
I've personally done this multiple times without any issue. Plus, in most cases EVEN IF THEY DO decide to enforce the clause, they have to give you notice of 30+ days to remedy. Worst case, transfer title back into your personal name, or refinance again... But incredibly unlikely.
Hope this helps.