How is the differential mode noise suppressed by adding a capacitor across the Lines
Most interfering noise on a cable is coupled equally to both conductors when certain cabling precautions are taken and these are twisting pairs (to reduce magnetically induced effects) and screening (to reduce electrically coupled effects).

But, to ensure you handle correctly the common mode voltages on both conductors in a pair, you need to have a balanced differential receiver.

The word “balanced” is key here. The balancing comes from both inputs having the same impedance to ground. If the impedances were not equal, most of the effort of screening and twisting is wasted.

Does a balanced receiver have perfect earth impedance balance? No, and that’s how a common mode interfering signal can result in a differential interference despite making great efforts with the cable.

However, any differential interference is usually high frequency and, this can be reduced by a differentially placed capacitor.

Also remember that an Earth impedance imbalance can be created at the transmit end so, if you don’t have an impedance balanced driver, all the great efforts in choosing the best cable and designing a decent receiver are spoilt by the transmitter’s poor characteristics.