I don't know the Gaggia, but on my Micro Casa I take the head group apart every few years and clean it. A surprising amount of buildup clogs the head. Can you take that apart and get the screen out to clean it?
It's part of the recommended regular maintenance in the instructions of my machine. I've not noticed any build up since I've been using a puck screen. I still have to take the thing apart to grease it every couple of years, but the group head has been much more clean.
If you do get it apart and cleaned, and it does help, and you're not using a puck screen, I recommend getting one to help keep the head clean. They're cheap.