Hi @Den K,
Unfortunately to my knowledge there isn't any method documented to clear the notification.
You can either remove the expired certificates or wait for the notification to be expired.
Notifications remain in the arbitration mailbox until they are removed by the component that sent them, or until they expire (they should be removed by the Managed Folder Assistant after 30 days).
Or you can use Search-Mailbox cmdlet in Exchange management shell to search the notification in arbitration mailbox and delete it from the mailbox.
First get the search result in administrator mailbox's inbox folder:
Get-Mailbox -arbitration | Search-Mailbox -TargetMailbox "administrator" -TargetFolder "inbox" -LogOnly -LogLevel Full
If in the search result csv file you are seeing the result like:
run the following cmdlet to remove the notification:
Get-Mailbox -arbitration | Search-Mailbox -deletecontent
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