If you're deliberately displaying the image in black and white, the colour pattern is interference that should be suppressed.

However, this practice was not universal, and archivists have now recreated colour copies (https://en.wikipedia.org/wiki/Colour_recovery) of some shows where only black and white recordings survived by reconstructing the colour from these interference signals.

There's no real luminance content above about 5MHz, and TVs used to notch out the colour at 4.43MHz.

As an aside, you can do all this digitally now with phenomenally sharp results.