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If you use the credit card to payoff a debt in a large amount, they would ask you about where that fund came from to pay off that debt. They usually run your report and that will give them the credit used for that account. They usually run again before closing too so plan accordingly.
They actually can get more than just a credit report. My Lender have their own credit agency and they do more than just pulling a credit report from the bureaus. Like UCC, Tax liens, judgment, suits, etc...