How to remove monitor artifacts in recorded video?

Hey guys, I recently recorded a scene which required me to film my monitor instead of using screen capture software and editing it in later. I expected the patterns you get in video when recording flat-screen monitors in some way, which was completly fine, however, it's a mess. If you watch the video on a large screen it's actually fine, but on smaller screens it's completly unreadable, which is a problem.

Is there any way I can fix this? Maybe use some kind of filter for this? I'd thought of maybe using the blur tool very slightly, but I figured I should get some advide from the pros first, as I just recently started using the Adobe suite of products.

Thanks in advance for your replies! 🙂