The vent has a flashing that's under the siding a few inches. It's used to nail it to the wall and prevent water from getting in behind it. You would need to remove the siding as it butts up to the vent over the flashing.
If it's vinyl siding you may be able to pull it off, remove the vent, replace the screen and reinstall. Same goes for aluminum siding but it's much less forgiving if you bend or crease it when removing.
I would reconsider crawling into the attic, if possible, with a piece of screen, a staple gun, and a can of wasp spray.