You can simply switch to another tab if you don't want to see those alerts, they are to inform you about challenges and events.
However, if you don't want to receive any alerts, go through these steps after you log into live chess:
Click on settings (in the black bar above), click on "Alerts" and change your settings as you wish.
at my alert there was this:
example:
"5|0 Blitz Tournament starts at 09:10! Click here to join! You can also click on the Tournaments tab to see all upcoming tournaments and events."
My question is, how to dissapeared that ?
long time ago, no message like that at my alert .
Thanks