Ditto what 10:55 said. We did that and Bank A matched the new offer.

GO back to Lender A and ask them to match B's offer.

I think you can generally withdraw a loan app and the issue is whether you have paid, or promised to pay, an application/appraisal fee.

This is probably a dumb question, but we're trying to refinance - we locked in a rate last night, but the second bank came back with a much better rate this morning.

At what point in the process do I have to decide which lender to go with?

Thanks!