If you cannot delete a message in eM Client and the same message “is not showing online in your mailbox webmail view”, then run the manual database repair which normally fixes that.
(To repair eM Client database manually for Windows) see @Gary post below from the following thread.
(To repair eM Client database manually for Mac)
Close eM Client and then “open the Terminal app via either Launchpad or Utilities” on the Mac. Then Paste and run the following command.
/Applications/eM\ Client.app/Contents/MacOS/eM\ Client /dbrepair
Then restart eM Client and see if that fixes it.
Note: If this is regularly happening could be a possible local mail database problem where you then might need to remove and readd your acct or create a new database and readd the acct.
Lastly if the message is also showing online and you carnt delete it online, then contact your mailbox technical support for assistance.