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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
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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.