A family of Microsoft word processing software products for creating web, email, and print documents.
The problem could be the result of an add-in that's installed on the affected PCs. One way to check this is to start Word while holding down the Ctrl key, and click the Yes button in the message box that asks whether to start Word in safe mode. When Word starts in safe mode, it's prevented from loading add-ins, the Normal.dotm template, and any custom settings that are stored in the registry.
If the extra mouse pointer doesn't appear while in safe mode, the next step is to shut down Word and start Windows File Explorer. Type or copy/paste this path into the address box:
%APPDATA%\Microsoft\Word\STARTUP
Press the Enter key at the end of that line. Windows will expand the %APPDATA% environment variable to the location of the profile of the currently logged-in user, and the rest of the address will bring you to the location where Word template add-ins are stored. If there are any *.dotm files there, rename them to change the file extension from .dotm to .bad to prevent them from being loaded by Word. Restart Word to check whether the extra mouse pointer is gone.
If that worked, start renaming the template files one at a time back to .dotm and restarting Word. If one of them causes the extra pointer to return, that one is the cause of the problem. You can try deleting that template and restoring a good copy from the original source (assuming the problem is due to some damage to the file), or contact the developer of the add-in for a fix.
Caveat: Word may also have COM add-ins that aren't found in the STARTUP folder. You can see what Word loads by clicking the COM Add-ins button on the Developer tab of Word (which you may have to enable in the Options > Customize Ribbon dialog). If you've checked all the template add-ins without finding the cause of the extra pointer, you can try updating or uninstalling the packages that included the COM add-ins.