I have access to more than twenty lenders: major banks, credit unions, and specialized lenders. I compare the rate, but also the value each one will accept for your property, the fees, and whether they’ll do an amortizing loan, a line of credit, or both together.
Your bank offers its refinancing product, with its own way of valuing your property and its own fees. If the value it accepts comes in low, you have no recourse, except starting over somewhere else. I can put your file in front of more than twenty lenders and find the one that accepts the best value and the structure that fits your project.