Will closing a credit card affect my credit score or ability to buy a house within the next year?

First of all, I'm looking at buying a house within the next year or so.

I moved all of my funds from a bank to a credit union a few months ago. I closed those accounts but had a credit card at the bank. I've opened a new credit card at the credit union which has an identical limit but a way lower interest rate with the idea that I would close the bank's credit card soon after transferring the balance. I've transferred the balance (and paid it off, woohoo!) but the card is still open and just sitting there. Can I close the bank's credit card without it affecting my credit score or ability to get a house loan? Or should I keep it open until after I've bought a house and then close it?