Sometimes, it is another bank offering the new mortgage. In the case that it is the same bank refinancing lower, they get a nice upfront chunk of money to do it, which they like. Mortgages always carry the risk of not getting paid back, or getting paid back in full, so they miss out on the interest, but a refinance is immediate money for them, and likely lowers their risk of the homeone defaulting, so they might make less, but they are lowering their risk.
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