Saylor Hayes wasn’t wearing a locator bracelet when her body was discovered — even though authorities say her parents told them she was … TMZ has learned.

John Herb Hayes III and Geordyn Nichole Hayeshave been charged in South Carolina with unlawfully placing a child at risk of or causing harm or willfully abandoning the child.

A rep for the Georgetown Sheriff’s Office tells TMZ … John and Geordyn told investigators Saylor — who was non-verbal and autistic — was wearing Project Lifesaver equipment.

Project Lifesaver is a brand that makes locator bracelets. These bracelets can help authorities to locate someone with special needs who goes missing by picking up a signal. Saylor usually wore hers around her ankle.

We’re told more than 100 people searching for Saylor were under the impression she was wearing the equipment and used that info to try and find her … but authorities say John and Geordyn gave inaccurate information — and searchers couldn’t find Saylor until it was too late.

If Saylor’s parents had been wearing the equipment, authorities believe she would have been more easily found.

We’re told they were also charged because they allegedly directed cops away from the river where Saylor’s body was found.

As you know … Saylor went missing from her family’s South Carolina rental home on Sunday — and was found dead Monday morning.