I've had this problem myself on my own email account and I attempted many fixes but never was able to remove the icon. I didn't want to go through a rebuild so I looked and tried everything else that I could. The icon would go away for a short time at times but would always return.
A fellow GW Administrator sent the answer to me and it was much simpler than a rebuild.
To start we are running GW Client version 22.214.171.124. I dug out my copy of GW 5.2 and installed it to a virgin workstation (no previous GW install). I then confirmed that I had read or removed all unwanted emails from my GW 5.5 email account. I logged out of GW 5.5 then logged into GW 5.2. And there it was an email that I know I had read and deleted some time before was still sitting in my Inbox. I opened and deleted the email and logged off 5.2 and back into 5.5. The icon was gone and hasn't returned since.
This is a neat trick to keep in your notebook for the future.