You can uninstall the MS plugin on Mendeley Desktop > Tools > Uninstall MS Word Plugin.
In your case, as you already uninstall the Mendeley Desktop, there's a way to remove by hand. According this thread/user, the steps are:
- Open up Word and click on the main menu in the top left, and then
select "Word Options" towards the bottom of this menu.
- From here
select "Add-Ins" on the left, and locate the "Mendeley-0.0.0.dot"
entry. The 0.0.0 number will reflect the respective version you have
installed. Next to it you will see the directory in which it is
located.
Here you can see more information about that too ("Citing Items in Word with the MS Word Plugin").