deleting smartobject background

You can mask the Smart Object Layer to hide the layers image content's background.  You can not change a smarts object hardened  pixels content with Photoshop Tools.  You can replace the Object  or open the objects to replace  an object's content with an image that has its background removed.

You can't delete anything in a Smart Object. Smart Objects are supposed to be non-destructive.

What you can do, if you want to remove something from a Smart Object, is to mask it by making a selection of the part you want to remove and add a mask using Layer > Mask > Hide Selection