Not to mention, would it not have also been a source of concern for her that her child appeared to have shrunk about a foot in height (which E.T.’s extendable neck could have fixed anyway)?
To be fair, Mary is a single mother distracted by a variety of other responsibilities on her plate, so it is understandable that an oddly shaped Halloween costume might not be the most pressing issue on her mind, but, regardless, it should not have been that easy for the boys to convince their mom that was her own daughter under there.
Whether the first thing you notice about the ghost costume is that the eye holes are inhumanly far apart or that the head underneath matches the figure of a 3 foot toad more than 7-year-old girl, it would be clear to even a stranger that it is not Gertie under that sheet, let alone a human child in general, so how does is this not suspicious to Mary?