One of the mods we made to our previous trailer was to add a push bar to the screen door. It not only gave us a good place to push the door open when going out, but it made it easier to pull the door closed behind us coming into the trailer. It worked so well that we installed one on the new trailer.
The push bar we selected was the same one we put on the previous trailer. This Camco screen door push bar is easy to install and it telescopes to accommodate different door widths. The bar comes with a template to allow the length to be set before it is installed on the door itself. A few holes into the door and screws to fill the holes completes the job.
It works great to move the screen door. I would not use it like a grab bar where weight is put on it.