From GitHub Support:

We have seen things like this happen before. Can you try a couple of things that should work.

Select the checkbox and see if there is an option to select all and mark all as done/read. If that is not an option, I have had success before with the REST API.

You can use the details from that API endpoint to find the unread notification and then the one below to mark them as read.

Activity - GitHub Docs

The curl command below will mark all of your notifications as read and with any luck will take care of that phantom message for you.

curl -X PUT -H "Accept: application/vnd.github.v3+json" -H "Authorization: bearer {token}" https://api.github.com/notifications -d '{"last_read_at":"2021-05-28T06:53:00"}'

You will need a Personal Access Token (PAT) to access the API from the command line. The PAT is used in place of the password to authenticate. To create a PAT follow the steps in the link below.

https://docs.github.com/en/github/authenticating-to-github/creating-a-personal-access-token#creating-a-token

Below that are the instructions to access GitHub from the command line using the PAT.

I hope this helps and please let me know what else I can assist with!

Cheers,
J.J.