What occurs if a homeowner has the funds to repay a mortgage but refuses to pay the bank, insisting on paying only the entity from which the bank borrowed the money? I’ve heard of a legal tactic some homeowners use to avoid repayment—how does this work?

Not sure who told you this, but even int he court of law if you go in for a dispute, the cost of funds to the borrowing bank (from which you took the loan/mortgage) would still be due. Your mortgage is a consent that you will pay the amount, and as such, the cost of funds to the borrowing bank is the very minimum you will have to pay if a dispute does go into your favor by a banking court, etc.