I personally clean my suppressors after 10,000+ shots. Our suppressors do not really need any maintenance unless they become damaged.
The product I like using on my airguns and suppressors, Is Ballistol.
I clean my suppressor every 10,000-12,000 shots.
Here is the link for a felt kit for the Suppressors.
Cleaning
1. Unscrew the threaded end of the suppressor.
2. Push the core out of the suppressor body/tube.
3. There is a felt sheet tapped inside with tape. Unravel the tape and remove the felt sheet from core.
4. Carefully remove the steel screen from the core. Caution the screen is sharp and can poke you.
5. Now you should have a bare core. Spray the core and steel screen with cleaner and let it soak for 10 minutes.
6. Brush the core and screen with a small tooth brush or similar to loosen the lead fouling. spray more if needed.
7. Rinse the core and screen and dry.
Assembly
8. Put the screen back on the core.
9. Wrap the Screen with the felt cloth snug, and replace the tape with fresh tape if needed. Replace the felt material if needed.
10. Insert the core back in the suppressor body/tube.
11. Reinstall threaded cap. now you have a clean suppressor.