The IMAP protocol has this silly concept of a message that has been marked as deleted but isn't really actually deleted.
The iPad only marks the mail as deleted. The IMAP client on the iPad considers this sufficient for the message to be gone, and you can't see it anymore when using that client. The web mail wants the message to be REALLY deleted before it goes away. If it's just marked deleted, it will still appear... with a strikethrough line.
To get the message to disappear from the web mail, you need to expunge deleted messages. The web mail interface might offer a way to do it directly, or else it will do it automatically when you delete any message from within the web mail interface. When messages are expunged, they are expunged all together, so it is enough to delete one single other message, and all of the other marked deleted (struck through) emails in the same folder will follow.