Well, for HMDA purposes, it doesn't sound like a purchase, as title to the home has already been transferred from Applicant A to Applicant B, prior to your loan. And it doesn't sound like a refinance, as the only loan that will get extinguished is Applicant A's, and he's not a borrower on your loan.
Applicant B's loan with your bank is secured by this home that Applicant A deeded to them? Or Applicant B already has a dwelling-secured loan with your bank that you will refinance with new money to reimburse Applicant A for the deeded house?
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I'm fixin' to fix that.