Thanks for your responses. The mortgage lender said it was no cost - which is a violation of RESPA. With joint marketing (mortgage lender placement on the realtor website) the cost must be shared - pro rata share. Then getting back to the way the lender is described on the website in the initial question. The lender cannot be described as "list of approved lenders" on the website?
"List of approved lenders" isn't necessarily a directly prohibited way to mention other settlement service providers that appear on a website of a settlement service providers, as far as I know. However, it does sound "eerily" similar to "Preferred" lender/provider, which has popped up in several RESPA cases as a phrase the CFPB has a problem with.
As you noted, the fact that your LO would get this advertising benefit for free is likely an issue, as the implication would likely be a defraying of expenses in return for referrals.