A lot. They know what your score is and "attributes" from your credit report. They see basically everything they'd see if they pulled a hard inquiry credit report. The good news is that it won't lower your score.

Hi Brad -

Banks are looking at your overall credit score which predicts how likely you are to pay back your debt. Mortgage and home equity lenders will take it a step further. They will look at your itemized debt to create a ration of your debt-to-income. Basically, they want to see how much money you have left after you pay you home mortgage, car, credit cards, student loans, etc. It's a good indicator as to whether you can pay your mortgage each month.
Banks also look for judgments and liens that would take primacy over your loan should you go into default. Lastly, banks are going to look at how many late payments you have and how much available credit you have on hand.