If you reinstall MS Office over the existing installation , you will get your office icons back .
Now, what is most important is to retain the icons there . So , I'd suggest you to stop using your third party registry cleaners (like tuneup utilities) . Only one program that I can recommend you is CCleaner - Free version . It doesnot delete the installer folder (where these icons and uninstallers are stored) like the others.
My Computer
At a glance
Microsoft Windows 10 Pro Insider Preview 64-bitIntel(R) Core(TM) i3-4130 CPU @ 3.40GHzCorsair Vengence 4GB x2 (8.00GB Dual-Channel ...2047MB GeForce GTS 450 (ZOTAC International)