You may need to run the script more than once with a reboot somewhere in the middle. You mention many different modules, so yes if Office depends on these modules then logically it would be removed last and it may just be that you need to remove all of those applications, do a reboot and running the script again. I know it is always a pain with remote users, but with an application as big as Office it is not as simple as just running a script once.
The leftover icons indicates something is still installed so run the script again. Or I would recommend getting a bit more specific so instead of "product where "name like 'Microsoft Office%%'"" try "product equals Microsoft Office 2010". Equals means the name has to match and you're effectively targeting a product like you would by removing it from Programs and Features in Control Panel. You know what you have from inventory (you can also get it by running "wmic product get name" from the command line to get the exact names) so script each one on a line, e.g.
Run your script:
wmic product where "name like 'Microsoft Office%%'" call uninstall /nointeractive
THEN REBOOT
Then run a second script:
wmic product where "name like 'Microsoft Office%%'" call uninstall /nointeractive
wmic product where name="Microsoft Office 2003" call uninstall /nointeractive
wmic product where name="Microsoft Office 2007" call uninstall /nointeractive
wmic product where name="Microsoft Office 2010" call uninstall /nointeractive
THEN REBOOT