Hi @PJMaycock , Welcome to our Community and thanks for your first post!
TeamViewer reproduces the partner side's screen, mouse, and keyboard - TeamViewer doesn't create a virtualization of the device which means that you and the remote side share the control of the mouse.
If you see the remote side moving the mouse, you need to wait they to stop using the mouse so you can move it.
If there is no one on the remote side, you can try disabling the remote input using the session TeamViewer Toolbar. (Actions ➜ Disable remote input)
Let us know how it goes and if we can help you any further. 🙋♀️ Best, Carol
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