Hi Miley,
Check this sample: JS Bin - Collaborative JavaScript Debugging from Dennis Seah which is an extended version of sap.m.Button. Where there is an extended property bgImg and method available for custom control as .getBgImg() by doing so you can fetch the URL of background image, also you can set a new URL using .setBgImg(). Is this what you are expecting?
Regards,
Sai Vellanki.