No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Happy Holidays and welcome to myFICO
I think you have to ask yourself a question. Is it worth the risk? And IMO, if I were in your shoes--no siree! I would not apply for any new lines of credit, which could jeopardize the refinancing.
I am not expert in the area, however I fully agree with CreditInspired - just not worth the risk. If I am not mistaken, mortgage lenders typically do a credit pull just prior to funding. I don't think you want to show inquiries, indicating that you are auto shopping at the same time. Even if it is not much of an issue, I could see where it could delay funding while they ask you about it.
Don't do it unless you're lender is aware of the proposed new monthly payment amount and that information was included in your Final Loan application that you signed Monday.