Hopefully they just meant they'll be checking your credit once and then will do a 'credit refresh' just prior to closing. The credit refresh isn't a hard inquiry that obtains new credit scores, it's just to get the most current balances & minimum required payments on your debts to make sure your debt-to-income ratio still qualifies. That is most likely what they meant, so you should ask them to clarify.
However, if they do end up doing a 2nd hard inquiry, then there is a chance your scores will change if it's outside of the 45-day window that opened when your credit was initially checked. This would be odd to do though, since credit reports are good for 120 days on most mortgage transactions so if you close within 120 days from the initial credit pull then your credit shouldn't be re-checked with a hard inquiry.
Lastly, with the latest changes in Fannie Mae & Freddie Mac financing, a 780+ score is now the "top tier" to get the lowest rates. See the chart below.
