hi user_1000,
I personally do not like it when anyone (person, business, corporate entity, etc.) tries to take up even one iota of my time with things or topics I do not need or want.
In the case of Avast!, I too, have seen what you have seen, even though Chrome is not installed here either. But, despite the above, I accept that Avast! is going to continue doing what they have been doing, soliciting for additional features, paid program adverts, etc., so as I accept Avast! as being one of the best a/v's available, that this is something that comes with the package. Not much I can do, or want to do, about this issue because of that.
If it really bothers you, please follow DavidR's advice and set the pop-up toaster window to the shortest time you can.
A glance is all it takes for me; but I make it a point to leave everything pretty much at default settings within Avast, with the exception of a point or two.
Ignoring this issue works just fine for me.