To be more clear, the ACCOUNT tab is always displaying a [1], like if I have one unread message. However, I don't.

This bug have been on my account since several months ago. Maybe 1 year.

At first, I thought it will eventually disappear, but due the GOG forum members high generosity who provide scripts to make the forum a better place, maybe is there a script that may help me to get rid of that annoy [1].

Suggestions?

I'd contact a blue one if I were you, support perhaps.
And if that makes feel you better, you're not alone ; )

I told judas and he suggested to refresh account but that didn't work. I didn't hear from him so I assumed he was going to look into it. It was on 13th April btw.

Perhaps ask the latest person that sent you chat message to send an 'asdf' chat message. Perhaps that will do the trick to clear the counter once you read it. If that doesn't work, try the person before that one that last sent you a chat message.

I just opened chat and immediately refreshed and the phantom notification went away!

Finally!! Thanks for sharing