Ogre Geargrabber’s control-changing effect ends during the cleanup step, at the same time that damage marked on permanents is removed. If you still controlled the Equipment at that time, this causes the delayed triggered ability to trigger. It goes on the stack and players can respond (which normally doesn’t happen during the cleanup step), then, once that cleanup step ends, another one begins.

Any ability of the targeted Equipment that triggers “whenever equipped creature attacks” won’t trigger. That’s because Ogre Geargrabber is already attacking at the time that Equipment becomes attached to it.

If the targeted Equipment can’t be attached to Ogre Geargrabber for some reason, you’ll still gain control of it until end of turn.

The delayed triggered ability (“When you lose control of that Equipment, unattach it”) triggers the next time you lose control of the Equipment for any reason, not just when Ogre Geargrabber’s control-changing effect ends. The Equipment will become unattached from whatever creature it happens to be attached to at that time. It doesn’t matter if Ogre Geargrabber is still on the battlefield at this time.