If it's a plugin, then there is no need for a file. But, you should make sure there isn't some file they uploaded via the use of a plugin.
Those errors are just showing warnings. And, if they are using a script, then that doesn't mean it is generating any errors that would show up in an error_log. You really need to look at your access_logs to see if they are accessing any scripts on your server that you don't know about.
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