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Hi mamajama, and welcome to the FICO forums.
Mortgage inquiries that occur within a certain time frame are scored as a single inquiry. In addition, mortgage inquiries are suppressed from scoring (that is, not factored into the score) for 30 days. These provisions were built into the FICO scoring models so that people wouldn't get penalized by shopping for rates at different mortgage lenders.
The length of the mortgage inquiry window is a little confusing. With the older versions of FICO, which include Transunion's TU98 score (which is sold here) and Experian's version 2 (not available anywhere), it's a 14 day window. All mortgage inquiries that occur during any 14 day period are scored as a single inquiry. It doesn't matter if you have 1 or 26, your score will only see the impact of a single inquiry.
With the newer versions of FICO, including Equifax's Beacon 5.0 (available here) and TU04 (not available to consumers but more widely used by lenders than TU98), the window is 45 days. This allows an even longer period to go rate shopping.
The suppression from scoring for 30 days is included in the scoring formula to eliminate the "first hit" effect that would come with the first mortgage inquiry.
Here's an illustration of how this works:
On April 1, you go to Able Bank to see if you can get a mortgage. They pull a credit report and score using the EQ Beacon 5.0. The score is 650.
On April 5, you go to Baker Bank to see if you can get a better rate. They pull a credit report and score using EQ Beacon 5.0. The inquiry from Able Bank can be seen, but it's not factored into your score - it's suppressed from scoring. Baker Bank also gets a 650 score.
On April 10, you go to Charlie Bank. They pull a report and score. Both inquiries from Able and Baker are on the credit report, but again, they're suppressed from scoring. Charlie Banks sees a 650 score.
On May 15, you go to Delta Bank. They pull a report and score. All 3 inquiries from Able, Baker, and Charlie are seen. Since they were all pulled over 30 days ago, they will be included in the score that is pulled. However, since those inquiries occurred within a 45 day window, they're treated as a single inquiry. The score that Delta Bank gets is 645 (hypothetically - there's no set number of points that are lost by an inquiry).
So to get back to your original question, running your credit again now won't affect your score if you're within the 14 or 45 day window and you're not beyond the 30 day suppression period. But there's no point in pulling it again unless you've made some changes that would actually improve your score (e.g. paying down a credit card). But if the lender waits too long to pull your score, then the first inquiry will be factored into your score and your score might drop.
One thing I don't understand - if your score is already at 625, why does the lender need to pull again? Also, did the LO tell you what your scores are for all 3 bureaus? You could also ask him/her which FICO models were used.