Thanks for the responses...
Essentially, Mortorola told me that they are aware of this idiosyncrasy. I quizzed them as to why I could not find another person who is experiencing the same thing. (hence, me asking to the many folks here.)
They said that it will be more common as people get new phones with the updated OS. They said there is nothing I can do about this. My phone is about 6 months old (that is when I got it.) They said older phones when updating OS will not see this.
I am no computer whiz but it sounded like bunkum to me. I hope I described properly what the situation is and they truly understood.
I sort of agree it is an app notification setting, but what app is it? I have looked at what I think it could be. I stopped by two T-mobile stores and the reps in the store (at least 40 years younger than me-LOL) and they thought the same thing but could not identify the app with which it might be associated.
Here is an image of what I am describing:
