It is a RF choke or ferite core. It will not allow high frequency signals to pass while allowing low frequency to pass.
The 60hz power is low frequency and does not know the core is installed. The arc at the brushes will cause the buzzing in AM radios and but noise on the AC line for other equipment to have to deal with. The brush acr is high frequency so it gets stopped.
The tool will work with or with it.
As the FCC gets tighter on this, much like emissions on gas engines you will see more and more of this type of thing.
When I bought my Oneway 2436 lathe, they have a RF filter option available. I bought it only to reduce the noise my variable frequency drive puts out. It does nothing for the lathe. Just trying to be a good guy in a noisy world. electrical noise that is.
Ed