I'm worried about this too as I will probably be buying a house this summer. I have a "real" job that pays well, but I also have income from the apps I sell. Even if you don't claim the income from your apps on your mortgage application to qualify for the loan, anytime a underwriter for a mortgage sees large deposits going into your account they want to find out where those came from. They want to determine that you are not borrowing money that needs to be paid back, and thus impacting your overall financial situation.
Please keep us posted on this as I will probably run into the same issue. This is not a stupid bank, I can almost guarantee any bank will ask you to verify large deposits when they are underwriting your loan.
Tell your bank that you don't work for Apple anymore than Britney Spears does. She probably has large deposits from apple as well.