This issue relates to Section 8 violations as detailed in RESPA, section 1024.14. The requirements prohibit any person from accepting a kickback, fee, or other thing of value involving a settlement service of a federally related mortgage loan.
Given your details above, it sounds as if the construction company’s placement of a lender’s name on their website would not be a violation as the bank/lender is not receiving a kickback, fee, etc. and the customer gets to select any lender of their choosing.
The second scenario doesn’t appear to be an issue either as the customer is the one benefiting from choosing the lender by receiving a lower rate or fee.
Careful consideration needs to be given regarding the relationship between the construction company and the lender. Is there any type of agreement between them that results in the lender or the construction co. receiving anything of value? The lender is providing a service that is considered a settlement service and shouldn’t be receiving any kickback, fee, etc.