In order to remove something in a photo, you have to replace it with something else (or crop off that part of the photo).
So in this case, you could replace the net with sky, but that may require 'cloning' over each individual strand...which would take forever and probably not look right in the end.
Another option would be to extract (cut out) the birds and branches and then place then onto a different background.
Here's a sample. I just did a very quick vector, not perfect by any means. I used a white background as I don't have any available shots of open sky to use. This is obviously a small version but if you want I can email you a .png or .psd file to work from.