Just because you have applied with a mortgage lender, that does not mean you are under any obligation to close with them. In fact, you are able to walk away from a transaction at any time right up to the closing table (and even three days after due to right of rescission laws in the case of a New Jersey refinance of a primary home). Lenders, however, may charge up-front application or appraisal fees. You will want to confirm with your lender at what point those fees are refundable, if at all, after application.