From memory you should be able to disable the tray icon from within the Realtek HD audio manager.
The other option is to completely un-install the Realtek software from Programs and Features, and manually install the driver only using Device manager, and manually pointing to the driver directory (usually a subfolder in the extracted realtek setup)
This is how i've always done it anyways, as I find the Realtek software a bit useless when all i really need is basic playback.