1. Pay off the card and get the loan.
2. Don't pay the card off and don't get the loan.
Unfortunately there is not a whole lot of flexability when it comes to Debt to income exceeding guidelines.
Some other ways you can explore to get your DTI in line with guidelines:
1. If you have MI look at a single premium option rather than monthly, it could get your ratio in line but will cost more upfront.
2. Instead of paying off the credit card look at buying down the rate or getting a seller concession to buy down the rate.
3. Opt for an Adjustable rate mortgage over a fixed rate
4. Opt FHA financing over Conventional
5. Explore a freddie mac approval rather than Fannie Mae (Freddie mac does not have a hard and fast 45% DTI so Sometimes a loan that cannot be sold to Fannie Mae can be sold to Freddie mac. Of course you have to be working with a lender that has that option available to them.
Those are just a couple of option I can think of real quick
They did not request you to pay off balance, pay off in full or anything other than CLOSE THE ACCOUNT.
It is about the credit you have access to, not what you are currently using. This is not a new thing. After granting you a loan, you could go and max out all the cards and get yourself into a mess. This is where American Express and Citibank often game the system by not revealing the credit limit and in the case of AE, there is no limit to publish.
Have your real estate professional suggest an alternative lender.