I see cleanup badge on my user page and it say :
how to get it :
that's all, not much info to help for trying to get this badge.
Do I need to back under a revision state under an edit page?
There is a very similar Q&A at Meta Stack Exchange that should provide the answer to this.
The accepted answer to How can I get the "cleanup" badge says:
A rollback involves using a command that is called "Rollback". It shows up when a post that you have edited has the most recent revision by another user. Rolling back will return the post to the last revision that you had made to the post. It requires edit permissions on other people's posts, but is always available on your own posts. For example, I have just edited your post. You should now have an option to "rollback" in the same area that you can flag or edit.
It can also be achieved on a post by rolling back to any revision, by accessing the revision history of a post that has multiple revisions (when you have edit privileges). The option "rollback" can be used to revert to any specific revision, and this qualifies for the badge as well. You can see this here on one of your own questions.