How did Talley (the private investigator) obtain the slipper Mrs. Almore had on when she died?

I thought George Talley was hired by Mildred's parents to investigate her suspicious death. But Marlowe says Talley must have taken the slipper Mrs. Almore was wearing (which hadn't been walked in, thus evidence of murder) from her body before the police arrived. How is that possible? He would've had no reason to be at the crime scene -- I thought he was hired by the parents because they suspected a cover-up. Am I missing something?