Hi Robert W.Looper,
Thank you for reaching out to Microsoft Community.
Dongles are uniquely and securely bound or programmed to the mouse or the keyboard and are sold as a matched set. Because of the secure binding or programming, we are unable to provide a replacement dongle that would work with the mouse or keyboard. Lost dongle is not covered by the Standard Manufacturer's Warranty also. Please contact support through our Global Customer Service phone numbers so you could check for replacement options available for the Microsoft Arc Touch Mouse.
If this answer your question, we highly encourage you to inform our Community by clicking on Yes or marking my post as an answer. This will help other members who may have the same issue as you. Otherwise, don't hesitate to update us so we can further assist you.
Kind Regards,
Marrion Y.