Thank you, kind sir. In LS's mind, she's good if she comes up with a reason for her every move, the reason doesn't need to make any sense, just need to 'splain it...
If the body was moved in the rental, dogs would hit on that, hence the knowledge of GS being deceased.
But the rental car also has GPS, LE would know her movements, and exactly where to search. And they have not found him yet.
IMO, the tampering with a deceased body charge can refer to simply hiding a body, not specific to moving it (or worse). I'm not convinced that she moved and hid the body to a "better place". So I lean towards the rental car was used to clean up evidence, which may include dumping bloody clothes and a chuck of wood. We don't know where these items were found, but I might guess it was at the snow sifting area on South Perry Park Road. LE knows LS was there for a period of time, IMO.