I don't use the Avast Ultimate product only the standard Avast Mobile Security.
If I have the Avast Mobile Security icon on my Home screen because it was always showing red ball with number 1 in it.
I never did find out why, but I suspect that it may have been because I did some customisations in the Avast notification settings.
In the end I moved it to another page. I had exactly the same thing on my Avast Mobile Security Samsung Android Tablet.
Are there two avast icons at the top of the screen ?
If so one is likely to be the notification.
EDIT: You could try reporting it as a bug. You could also try sending feedback in the app, reporting what appears to be a phantom feedback notification in the icon display. I have just done that.