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First of all, there is generally no such thing as "ASAP" in credit. However, there are a couple things you can do right now.
The scores that you mentioned, are they FICO scores? If not, they have little use as FICO vs non-FICO(we call they FAKOs) can be a big difference.
Easiest thing and probably the fastest is to pay that CC down. Currently, you are at 88% utilization. That is considered sky high around here. You want to pay it down under 10%/$250 to maximize your scores.
Since you only have 1 credit card, opening another 1-3 will actually increase your score. Actually, your mortgage officer will probably suggest you open a few cards anyways to get you approved.
Regarding the late, you can also call the credit card company and ask them to remove the late off your credit report, since this is your one and only late. Some will take this request over the phone, others will require you to write a letter in. What credit card company do you have? There is a stickied thread over at the CC forum with backdoor numbers to majority of the CCCs. I think its common that CCCs have some sort of policy for removing 1 late payment as a courtesy.
I have capital one and I called the 1-800 number and they told me they dont remove late payments.
did you call this one?
Cap 1: 800-707-0489 (Senior Escalation Account Mgrs.)
I've had them remove a late payment on my CR with a 3 minute phone call
Try the backdoor number above and try to get that removed. If the phone call doesn't work, I'd start a campaign of snail-mail GW requests.
Remember, you are asking for "goodwill" .. try to remain patient, gracious, and kind.. you're basically asking for a favor.
And having a $2200 balance on a $2500 card is killing your score. That's 88% utilization. Pay that down to less than $225 and you should see a wonderful boost in your score, as long as you don't have any other big bads in the way.
How soon are you trying to get a mortgage?
Beg and plead. Call different times of the day to see about getting a different Rep to answer. Call them by their name and grovel.
Ya that was the number I called, I will try a few times though and mail letters if I have to.