Help Identifying Frost Free Faucet Manufacturer

The screen is just one part of an aerator. There are a few different components to an aerator. It's best to get a new aerator instead of trying to track down all the individual pieces. It'll be worth the little bit of extra money. To make sure you get the right aerator the first time, I recommend that you bring the old one into the hardware store to match the threads.

Worst case is that you bust a soldered fitting (very difficult) and have to open the wall up, which you would have had to do to replace a soldered fitting anyway. Since your water is already shutoff, give it a hard turn and see what happens.

Personally, I'd open the wall up even if it's threaded and sealed with pipe dope. Because after you replace the faucet, you want to check for leaks. It's much easier to do a little drywall patching and painting than it is to cleanup the water damage from a slow leak that goes unnoticed for days. You can also make sure the insulation is tight around the pipe so that there isn't a chance it will freeze in the winter.