One of the most useful tool for isolated objects and almost no one pay attention is the Color Range
After you open your document, you can find this tool in the upper menu, in select/color-range
This powerful tool gives you the ability to isolate that background that is almost white but not totally. By selecting with the eyedropper tool what you want to delete this powerful tool will create a mask of what is necessary and then you can easily erase the background.
Give it a try and see how easy that is!