1. You can pry the screens out and replace them. Or even leave them out. You can probably get replacement screens online easily enough or from a local vendor.
2. If you have rust deposits inside the solenoid (the part that automatically lets the water in and shuts it off), you could try getting some CLR in a syringe and squirting it in the inlet.
I may try that. It is laid on it’s front side. I put a cap full of white vinegar (have no CLR at home). The screens are out but the vinegar is sitting there.
I will see if I can figure out how to get the back off the thing. Screws and clips.