It’s not a ground filter, but a virtual ground. The point is to divert current from whichever power rail is further from ground, into the ground from the input

It’s not a ground filter, but a virtual ground. The point is to divert current from whichever power rail is further from ground, into the ground from the input device. That makes it so that the two “main” opamps see a common mode voltage of 0V. Opamps generally perform better near that point. I’m not sure that it’s really necessary here with modern op amps, and the author may have just copy-pasted the circuit from somewhere.