Reducing that resistor to 1k means the input impedance is now 1k instead of 10k.
I am sure that more experienced engineers can explain in a more "proper" way, but with my words, I would say that means it requires more effort (current) to make the voltage move on the input, and is therefore less sensitive to ambient (fx electromagnetic) noise.
Problem is with a low impedance input you will get less sound from a high impedance source. For example a 1k ohm source will create a voltage divider with your input impedance:
source -> 1k (source's output impedance) -> cable -> 1k (your circuit's input impedance) -> GND
That divides your voltage by 2, i.e. you get 50% of your source voltage. With a 10k input impedance you would get 91% of the source voltage.
But since your TV output is made for headphones (which can have as low as 32ohm input impedance), it probably means your TV's output impedance is only a few ohms, so with 1k you should be fine.
Hope that makes sense
EDIT: actually if you have ever heard a massive low frequency noise coming out of a guitar amplifier when no guitar is connected to it for example, that's typically the 50-60Hz, and it's because of the way guitar microphones are made the input of a guitar amp has a very high impedance (usually 1M), so is very sensitive to noise.