SP probably didn't care about tools as long as s/he was wearing gloves (heck, I would have had two sets on). No fingerprints. I wouldn't want to have to worry about carrying bloody tools (at least anymore than absolute necessity due to possible Identification factor) with me to dispose of. I mean, I already have enough to dispose of with the bloody SwatPerp outfit/boots/shoe covers/helmet which have DNA AND Missy's blood and possibly SwatPerp's blood if s/he got cut/injured in the assault.
Agreed, and maybe in their head, if they were trying to make it look like she was killed during an interrupted robbery, they wanted the "robbery type" tools left to further ensure that LE assumed it was the thief who killed her??