I sent HTC a complaint and they promptly replied with the following:
"Kindly note that this application is considered to be pre-installed application. Unfortunately, the preinstalled application on your phone is considered as a system application and cannot be removed, however you can search over Android Market for an application that would allow you to control your system files and remove\disable such application from your system."
We all know that does not work, but they suggested the following as well:
"However, you can set this application on silent mode and disable all the notifications from the settings by following the below steps as a temporary solution:
Menu -> all apps -> Al-Moazin ->
Then please click on the microphone found at the bottom until this silent sign appears. Then press on menu -> settings -> disable all reminders and Times Adjustments. Then please perform a soft reset for the phone by removing the battery and then re-inserting it."
I've tried the above steps, and it stopped the notifications. Now the screen only mysteriously lights up five times a day.
Important: when soft restarting the phone, the battery must be suddenly removed, do not shutdown your phone.
They also promised that an update will be released soon without these sticky applications.
The lighting up is most probably the app pulling a wakelock, but not having any notifications. It is a poorly coded app in this sense...
I'd suggest that you root the phone to remove the app.