There is/was police speculation that the mom bought the ligatures weeks before. There is also the fact that the Ramseys were given plenty of time to themselves after the investigation had actually started. Could have fairly easily disposed of it, jmo.
Also, she was tied up entirely for show. The police said there was "
staging within staging" of the body, i.e. she likely was not raped and/or tied up while she was alive, but just made to look that way. There's also the fact that killer used duct tape, but left behind no fiber or DNA evidence. The only cloth on the duct tape was strongly suspected to belong to the coat Patricia was wearing the night of the murder.