Lowering the noise

I am shooting my 10/22 into a target mounted on a steel trap designed for .22 ammo. Besides the shot itself, the trap makes an infernall sound when hit with a bullet.

How would I go about minimising the noise? Would it help if I glue some kind of material outside the steel trap to absorb sound and vibrations? Any other ways to reduce sound?

Would 10/22 cycle properly with subsonic ammo? If not, what is the quietest ammo I could use?

V.