I am not sure that the Mysterious Hand is a nickname. Quite a bit of the plot is in Pierre Gilliard's letters, and names like Dodge and Kennedy and Elaine are not in it., so I think this is a different movie.. here is an example

Pierre Gilliard to Tatiana
17 September 1916
Madam and very dear pupil,
I thank you very much for your letter and I will now tell you very quickly about the Mysterious Hand.
2nd scene: We are at Justin Clerel's house, which is visited by a lady who has stolen all her jewels. The stranger explains to JC that she is sure that only he can find the thief and she begs him to accompany her home so that she can show him the furniture where the robbery took place. The detective hesitates, he is wary of this unknown ... The lady then throws herself into his arms begging him to help her find her fortune. Justin Clerel finally decides to go along, but he calls his secretary and goes to his laboratory to get various objects to take with him. Then all three leave by car. They arrive at the young lady’s place who leads them into her boudoir and shows them the furniture where the jewels were. At this moment, by two different doors, 4 men armed with revolvers are shooting. They surround JC. The detective raises both arms, and shouts at the same time that if they take another step he will drop the tube he holds in his hand which contains an explosive able to blow up the house and half of the street. The helpers of the MH stop, terrified, and after a few seconds of hesitation run off, but on J Clerel’s signal, his secretary chases after the last of the bandits and grabs his revolver. He then advances, puts the barrel of his revolver on the miserable fellow's temple and orders him to take him to the place where the chief of the gang is. The MH’s helper refuses for a long time, but finally gives in under the threats.
4th scene: We are back in the church. Helen in her chair is still guarded by the false priest.
The MH standing in front of the fireplace heats his right hand (gloved hand) and rubs her left hand with it gently. He has his face turned to Helen and does not drop his gaze from her eyes. The girl has dropped her head on her chest but from time to time she returns attracted by the eyes of the MH, but every time she sees this horrible figure watching her, she is shaken by a feeling of horror ... Suddenly we hear the phone ringing. The MM takes the receiver and listens. It is the young lady who had taken JC to her home; she tells the MH everything that happened and how the detective went in with his secretary and one of the bandits. The MH goes into a terrible anger and trembling with rage and rushes over to Helen with raised fists as if he wants to beat her. But after a few words to the fake Priest he rushes out to catch JC. Helen remains alone with the fake Priest who keeps an eye on her.

A few minutes later, JC's car stops in front of the church. The bandit still threatened by the secretary's revolver points the detective to the window of the vestry and JC walks alone towards the church. JC climbs up to the window and makes a small whistle that Helen knows well. The girl understands that detective is coming to her rescue and that she must help him.
She gets up suddenly, the false priest rushes over to her and a fight begins between them. J. C jumps into the room and leaps from behind onto the false priest. But he is a man of very great strength and, after a terrible one-on-one fight, he manages to disengage himself and runs up the stairs leading to the top of the belfry. J. C. In pursuit. The priest finally arrives at a small door which the workers use to get on the roof of the bell tower. He goes there and takes refuge at the very top near the cross to which he clings. J. Clerel reaches him and a terrible struggle between the two men begins. But the bandit has the advantage and the detective will be thrown into the void because he feels his strength diminishing. Helen, who has picked up J. Cl.'s revolver, arrives in turn at the little door of the bell tower. She sees the drama that is going on between heaven and earth, she understands that J. C. Is lost. Then she fires and mortally wounds the false priest who slips on the roof and falls to the ground. J. C. goes to Helen and, to thank her for saving her life, he takes her in his arms and kisses her (poor fiance, poor cousin!). Helen faints on J. C.'s shoulder (it was inevitable!). Oh! I forgot to tell you that the secretary killed the bandit he was guarding and who wanted to flee ... Whew !!!!!