intuitive answer:

Consider a system with a square wave (up to 9th harmonic for sake of discussion)
and some additive noise. (call it white noise that terminates at the 6th harmonic)

Filter the signal and pass the 1,3,5 harmonic.

What happens?

1. The rise/fall edge of the square wave occurs over a longer period of time.
2. The in channel noise remains the same.

Now since the same noise is present on a signal where
the rise/fall of the edges is greater, the apparent jitter
of the transition edge spreads out more.

Intuitive enough?

(No equations were produced in this explanation.... )

:)

How can it improve something that is not there?

Any filter takes away spectral content.

If HPF, which is commonly used to get rid of a DC bias, and you set the filter break point below the fundamental, you have not removed signal content.

However, if you start to take out the fundamental, your resulting signal is going to lose it's rise-fall edges as well.