In the scanner rewind (
Websleuths Crime Sleuthing Community) they ask about whether she owns such a pet, confirmed and asked when last seen, said 8:30 from the rec center walking south, which I took to mean that a witness remembered seeing her walking south with the pillow pet, and the witness viewed this from the rec center.
Then when they say the pillow pet is "on scene" and she would have had to come "back here", I figured that meant at home, since that was the only place she could have come "back" to. (Also because the direction of the question about whether she had such a pillow pet, followed by the answer that it was "on scene" implied to me that they were at the house.)
I also recall reading somewhere a more detailed account of this incident, in which the mother goes and fetches the pillow pet in the house, but that may have been someone giving their explanation of what they thought happened, rather than any actual knowledge.