None of the articles I've read on Beta Crux (Mimosa) mention it's tiny crimson companion.
It's only an optical companion (not gravitationaly bound), but with a color index of 3.5, it's the reddest star I've seen in a scope!
Mimosa is 600 times brighter than this carbon star, so I need to stop the scope down to f10 (using an aperture mask) in order to see it! The view of Mimosa together with the Jewel Box Cluster thru a low power eyepiece is stunning.
But the Jewel Box looks it's best at high mag (>50x).
Also, having a Mimosa cocktail while observing enhances the view.

Canon G9X, 90mm/f5.6 Achromatic Refractor
Eyepiece projection at 20x
2.5s@ISO3200

Image cropped and enlarged.