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That still sounds like a solution when you're restricted to only accessing one side of the door. They might be able to rig something up before they leave the room that is much easier to execute after they close the door and without looking.

A string with adhesive, attached to the end of the chain, run over to the open door and under the edge of the locking plate. Then under the door. Close the door, pull the string, door is locked and string comes off. No evidence, takes two seconds. It might need a little tweaking but sounds plausible.